Urahara, as master of the hogyokyu, knows the limits of Aizen's soul [and power] and knows he must be pushed to his evolution limit before he can be dealt with.

Aizen thinks Gotei 13 and co want to push his Shinigami limit and have him evolve to the next level and then have Ichigo kill him. He doesn't know about his multi-stage evolution, so he wont let the Gotei 13 he despises be the ones to push him to transform. Its why he used Kyouka Suigestsu against them, so all the damage they would have done that would have pushed him to reaching his limit didnt occur. Yamamoto knew this and so did a double gamble, using Ennetsu Jigoku to make up for each beaten member's damage and to add it all at once, or in the case he was beaten, Yamamoto used Itto Kaso to add the needed Gotei 13 damage contribution. The whole plan. according to both Aizen and the Gotei 13, was to push Aizen to evolve quickly and have Ichigo beat him so that Urahara's Kido would take effect, neither of them knowing Urahara duped them since Aizen was multi-form. Then when Aizen transformed by the Gotei 13's hands to Cocoon, he would be pushed over by Gin into Larvae (what they thought was Final) form and then Ichigo beat him. But Gin knew Aizen had at least one more transformation, which is why he didnt use his true Bankai until Post Chrysalis Aizen and focused on pushing Ichigo.

He tells everyone to fight him and damage him so he can be pushed to his limit and evolve to the next stage. Then in the next stage, him, Isshin and Yoruichi would let off on him and push him into the next stage. Then Gin is supposed to push Aizen to his next form. Then Ichigo, who is one stage outta cocoon stage, will beat Aizen and push him to his last form and soul limit. Aizen will then no longer be able to evolve and Urahara's seal can work since Aizen has no more hidden power and the seal freezes him at thie stage it takes effect and all the power of that stage. If the seal had activated when Aizen was in a cocoon, then when Aizen evolved he could have broken out. Therefore it was necessary to push Aizen to his power limits and push Ichigo towards his and have him evolve too so he can beat Aizen. Thats why Aizen was sealed when he was and Urahara was alive. He planned everything out-Aizen's soul's limit in power and potential to grow-when Aizen seized the Hogyokyu back in SS Arc. Then, when Aizen rebelled against the Gotei, Urahara could use their help to push and defeat Aizen. Urahara used the Gotei 13, Yoruichi, Ishhin, Vizards, Gin and Ichigo so he could seal Aizen and get his Hogyokyu back. He knew Aizen's evolutionary path and the forms he would take as well as his limits. That was why everything fell the way it did. The Gotei13 and Vizards push Aizen's Shinigami limit, Urahara, Isshin and Yoruichi push Aizen's cocoon limit, Gin pushes his larvae form, and Ichigo pushes him into LIMIT Final Form. Then Aizen, with no further power, would be sealed away by Urahara's Kido Seal. Ichigo was to be pushed to his Shinigami limits by facing and defeating Gin and his Bankai who was a powerful Shinigami up there towards Kyouraku and Unohana. Then Ichigo would be pushed over his limits and cocoon in the Dangai [3 months in 1 day, plenty of time for Zangetsu to push Ichigo to his cocoon and through that phase as well] and Ichigo comes out in his larvae state. Urahara stayed in contact with Isshin who stayed in contact with Zangetsu and updated him on Aizen's power output so Ichigo could be made to match if he was lacking in Dangai. [Ichigo in cocoon state couldn't beat Aizen post Larvae but Ichigo's larvae state could beat Post-Larvae state.] Soul Evolution is Shinigami/Hollow/Human-Cocoon Phase-Larval State-Butterfly State-Deathfly State-Final Form

Aizen Chart:

Shinigami Form

-Takes Gotei 13, Vizards, Ichigo, Isshin, Urahra's kido barrage to push Aizen into Cocoon Phase. Gotei 13 supposed to bring Aizen uptowards Cocoon Phase but were beaten by Kyouka steps to make up all the damage they should have done, but Aizen sees through him and sics Wonderweiss on him to beat him, so his Shinigami limit wouldnt be met by the Gotei 13's power. But Yamamoto gets one up on him when he pulls out Itto Kaso, which makes up about 1/3rd of the damage needed to push Aizen. Then Ichigo contributes with a Hollowfied Getsuga Tensho, and Isshin cleans house and pushes Aizen to 1/2 limit and he begins to cocoon. Urahara then shows up to push Aizen to full Cocoon Phase and plant the seal in him by embedding it into his Kuyoshibari Bakudo, then pushes Aizen up higher to his limit by using Hado 91. Then he finishes him up by placingh the reiatsu seals which push Aizen into Cocoon Phase.

Cocoon Form

-Isshin, Urahara and Yoruichi 3 way combo him and push him towards the limit of the power he has in Cocoon Phase and then Aizen evolves.

Larvae Stage

-Gin uses his bankai Kamishiri no Yari to push Aizen to his Larvae state limit, which proves Gin's total limit since his full on Bankai pushed Aizen's Larvae state when Isshin, Yoruichi and Urahara 100 years rusty could barely push Aizen's Cocoon Form. Gin's Full Power Potential equals Isshin, Yoruichi and Urahara in Shikai level 100 years rusty.

Butterfly State

-Gin is killed, and Ichigo in Larvae state arrives to push AIzen into the Deathfly State. Ichigo's Larvae State defeats Butterfly Aizen.

Deathfly AIzen

-Transforms and seems 10% weaker than Larvae Form [Post Dangai] Ichigo. Ichigo could beat Deathfly Aizen still, but chooses to go overboard and use Quincy Letz Stil: FGT (Final Getsuga Tensho)

Final Form AIzen

-Transforms into after being hit by Mugetsu, which blows past Deathfly AIzen's limit. This is Aizen's highest power and final evolution (he's shedding into it before the seal takes effect, which is why he looks difference during his sentencing) and he has nowhere else to go. He'a at his peak power in total soul, and is thus able to be sealed since Aizen's reached his truest limit. Aizen is sealed by Urahara's Kido Seal, and Urahara can retreive the Hogyoku, and be rid of Aizen and his machinations that got him exiled. He also gets to research Ichigo's potential since he transformed into only Larvae state and could beat Aizen's second to Final Form, meaning Ichigo's levels of power to AIzen are 3 dimensions removed.

During the Quincy Arc, Ichigo is brought back down to his Shinigamni Limit state, and must be pushed past this limit like Aizen was by being trained by Zero Division and pushed into Cocoon State. This all wasn't seen first time since it happened with Ichigo vs Zangetsu, but in the War Arc, he is being shaped to the next level by the enemies and training around him. Then he is pushed into the Cocoon Form by Ywach's Sternritter Uryu fights Ichigo at his Cocoon Limit and push him back into Larvae state (Post Dangai but improved Zanpakutou) and a new Bankai thats not FGT but similar in power. Ichigo then fights Cocoon Form Ywach who is pushed into Larvae form by Ichigo. Ichigo Larvae state fights Ywach Cocoon Stte and Ywach transforms by fully absorbing Soul King's parts except one. Ywach Larvae state stomps Ichigo Larvae state but Ichigo activates Bankai and draws with him. Ywach evolves again through Quincy power and enters Butterfly Form, and Ichigo is made to follow by Hogyokyu while new Gotei hold off Ywach and pushes Ywach to Deathfly State. Then Aizen and Ywach square off, and AIzen pushes Ywach to Final Form. Then Ichigo leaves in Final Form and duffs Ywach's Final form and destroys him in some way. Then Aizen is still there in Final Form, but he's no match for Final Form Ichigo who is 3 dimensions removed from Aizen. All that's left is to replace the Soul King, which either Ichigo will do or more likely Urahara, who will use all his compiled research on Aizen's evolution, Ywach's evolution and Ichigo's evolution to achieve 7 Dimension Final Form as well and take over as Soul King using his Hogyoku to achive Perfect Resonance with it and completely become one with it so it cant reject him. Urahara, as mastermind of this plan and Aizen's downfall all while seeing the Soul's Transcendence Limit, and as being able to outhink Aizen and keep up with Aizen's Cocoon Form while still in rusty Shinigami Form, points to Urahara being the most powerful character bar Ichigo.

Soul State

Shinigami/Hollow/Quincy/Human

Urahara (Fake Karakura, 100 yrs rusty, kept up with Cocoon Aizen, no peak power found yet), Ichigo (took Gin and Zangetsu to transform/ took Zero Squad & Sternritter to transform)

Aizen (Fake Karakura, took Shinji, Rose, Love, Kyouraku, Hitsugaya, Sui-Feng, Yamamoto's Itto Kaso, Ichigo's Getsuga, Isshin zanjutsu, Urahara's Bakudo 61, 63 and 79, Hado 91, and Urahara's Reiatsu Seals to transform), Ywach (took absorbing Mimihagi-sama to transform)

Cocoon Phase

Ichigo (Inside Dangai vs Zangetsu/ to transform/ took Uryu to push Ichigo to transform), AIzen (took Urahara Shikai, Isshin Shikai and Yoruichi Shikai Hakuda Lvl and Shunko to push Aizen to transform), Ywach (took absorbing Soul King's parts triggers him to transform)

Larval State

Ichigo (Emerges from Dangai after 3 mo battle with fake Zanpakutou/ takes down Ywach Cocoon State), Aizen (Vs Gin's Kamishiri no Yari which one shot Aizen's Larval Form and allows him to transform), Ywach (took drawing with Ichigo's True Zanpakuto Fusion to transform)

Butterfly Form

Aizen (took Ichigo's Post Dangai form to transform), Ywach (vs Gotei 13 full power and Bankai as well as Forbidden and Hidden Kido, Xcution and Ganju), Ichigo (assisted by Urahara to reach)

Deathfly Form

Aizen (took Final Getsuga Tensho to transform), Ywach (took Aizen's full Final Form power to transform), Ichigo (assisted by Urahara to reach)

Final Form

Aizen (rejected by Hogyokyu), Ywach (defeated by Ichigo [and Urahara], Ichigo (assisted by Urahara to reach), Urahara (absorbing Soul King parts into Hogyokyu and holding Soul King's Mind which he also gives to Hogyoku, Urahara resonates and becomes one with Final Perfect Hogyokyu and becomes new Soul King and jumps to Final Form)

Urahara set out to become Soul King by plotting out how to remove Aizen-who had had him exiled from Soul Society-the exact moment Aizen seized the Hogyokyu from Rukia,.Urahara had mastered the Hogyoku by the time he placed it within Rukia's gigai and so learned about the Soul Transcendency from the Hogyokyu that Aizen had which, once he embedded it in his chest , told Urahara Aizen's transformations, how many and their relative limits. Hogyokyu is an artificial heart of the original Soul King which is why it has a presence but no discernable reiatsu as noted by Tessai. Urahara, as the Mind of the Soul King, wished to become whole again and so used the Hogyoku to learn how to turn its Shinigami vessel into the same dimesnion as the Soul King (7th) and absord the other Soul King parts to be reborn as the True Complete Soul King. Its why the Soul King stirred when Ichigo arrived since Ichigo's transformation data was needed to back up Aizen's transformation sequences and deal with Ywach who threatened Urahara's position when the old Soul King was offed. Then through orchestrating both Aizen's and Ichigo's growth to Final Form 7th DImension, Urahara not only got to see the results without enduring any personal mishap, but he got to eliminate potential threats to his power as well through Ichigo, who will act as his Zero Squad Captain. Since Urahara's full Shinigami power will probably equate to at least Larvae Aizen, he is 2-3 dimensional planes ahead of even Ichigo.

Urahara (Shinigami State=Larvae Ichigo, Final Form Ichigo=Larvae State Urahara, Urahara 3 Dimensions Ahead in Power)

Ichigo (Larvae State=Deathfly Aizen, Final Form Aizen=Butterfly Ichigo, Final Form Ichigo=Larvae State Urahara)

Aizen (Final Form=Butterfly Ichigo)

All three had the potential and power necessary to reach the same plane as the Soul King, but it was Urahara's intunement with the Hogyoku he created which awoke the Mind of the Soul King within him that allowed him to go further than the others. Urahara ascends instead of Isshin because of the Mind of the Soul King being burdened by him, asleep like Mimihagi with Ukitake, which eats a shit ton of reiatsu but Urahara is stronger than Ukitake because he is improved by the piece, not hindered like Ukitake was. That means, Urahara at his max w/ MoSK would still not be full Shinigami Power due to the sealed reiatsu keeping MoSK inside, MoSK being mastered by Urahara unlike Mimihagi-sama by Ukitake increases Urahara's soul potential greater, allowing him to surpass his Shinigami limits unlike Yamamoto, Unohana and Zero Division. Yamamoto was brought to his Shinigami Limit, but had no catalyst to evolve since nothing beat the power of Ryuujon Jakka/Zanka no Tachi. Zaraki Kenpachi may be a potential candidate to Soul Transcend as well, given that his sealed sword Shinigami state beats Unohana's full power, and his Shikai state can cut a large meteor and a dimensional plane of space.