AN: Alright, this idea has Izuku having a version of his mom's quirk. She can levitate anything to her hand so long as it would fit in her palm (from my understanding). Izuku has full telekinetic control over his small objects although there is a very small weight limit instead of just fitting into his palm. This is something most would write off as a quirk too weak for Hero work but Izuku is clever and hardworking. His best friend is going to be Kirishima who moved to Izuku's neighborhood as a little kid and they became close. Izuku is going to be like Mirio, a seemingly weak quirk that he worked his ass off with to become talented. Kirishima I see more like Nejire, a quirk that starts super weak but becomes really strong through intense training. We know Nejire's is using her stamina to create those blasts of energy so she had to train to get her stamina up enough she could use it effectively. With Kirishima we see his hardening attain new levels as he trains with it. During a flashback to his younger self, we saw how weak it started out as, so we know that's how it works. I don't know of anyone in 1-A, 1-B, or general Education who has a quirk in similar line to Amajiki but I'm willing to listen. Anyway, this story will have Izuku and Kirishima working to become like the big three.
AN2: For how I'm portraying Aizawa and All Might in this I see it as actually pretty in character. All Might was willing to hold off giving One for All to Izuku until the literal last second, mere hours before the exam, and not giving the kid any real experience or training with the super powerful and dangerous quirk that he himself said could blow Izuku's arms off if he wasn't careful. As for Aizawa, we know he's expulsion happy and there's no way he wasn't sabotaging the scores during the Quirk Assessment test. Or do you expect me to believe weak, runty, lazy little Mineta was able to do better in physical fitness than Izuku Midoriya, who was able to run with a full sized all might on his back BEFORE getting a quirk?
AN3: This is going to be multiple little clips from various points throughout the story.
Through Hard work (Working title)
-Nezu-
Frowning, Nezu stared into the eyes of his apathetic 1-A homeroom teacher as well as his newest faculty member, All Might. "Denied." Nezu was in no mood for games or jokes after their request, "I'm not kicking out students, before the school year has even begun mind you, just so you two can have your favorites join the Hero class. They didn't make the cut so they can try to get into the hero course during the Sports festival." Glancing down at his desk he saw two folders, each man having requested that their pick be added to the hero course.
Aizawa had chosen one Hitoshi Shinso who had failed the Hero entrance exam but passed the General Education one. The boy's quirk wasn't good against robots, which had worked against him, but so had the boy's lack of physical fitness or determination to train his body. Still, Aizawa wanted that brainwashing quirk nurtured for underground hero work.
All Might on the other hand wanted his successor, one Melissa Shield, added in. Apparently, he'd been training her body up so she could receive his quirk but the goal he'd set for her to get it had taken a bit longer than expected and, when combined with a missed flight, she wasn't able to make the entrance test in time. Thus, All Might coming to him.
"I can easily just expel a couple of them on day one." Aizawa deadpanned, pulling out two more folders "These two have weak quirks, and the reports from their school show a lack of discipline and value. Hell, the telekinetic boy just used his powers to turn the off switches."
"Aizawa, let me be clear." Nezu's tone left no room for nonsense, "You've used up your last straw with me now. You'll have these two in your classes, but they and everyone else will also know it was only through your nepotism and that you tried kicking out two students who hadn't even gotten to day one yet. These two boys, Midoriya and Kirishima, will be in a new class so they can get more focused attention since you want to play favorites so badly. Also, you've lost any right to expel students from now on. You may make a request, but your punishment authority is gone. Now both of you get out of my office."
-Sports Festival final Round-
-Nezu-
"And first up, we have Melissa Shield of Class 1-A against Izuku Midoriya from class 1-Z!" Present Mic shouted from outside the booth where Nezu sat with All Might and Recovery girl so they could openly discuss One for All as needed.
"I still can't believe you denied her support item request." All Might Scowled over at Nezu, the principal calmly sipping his tea unphased.
"She requested a powerful support item that, yes she made it herself, is also a crutch. She's used those Full gauntlets every time her quirk was active while at this school, never actually working on improving her control over her own quirk. The only support item being allowed for a hero course student is the young Aoyama boy due to a medical issue, not a lack of training or control."
"I'll make sure the first aide wing is set up for her and the boy she's fighting." Recovery girl sighed in exasperation as the fight began. Melissa let out a punch with a yell, her arm breaking from the force of it even as hurricane like winds rocketed towards Midoriya who, quite literally, flew out of the way.
"What?!" All Might gaped at the sight of the flying boy "I thought his quirk was weak telekinesis!?"
"Oh, it is." Nezu smirked as the boy thrust his arm forward, the ground ripping itself apart as force and debris sent the broken armed Melissa Shield out of the ring in one move in the fist round, "You see he can only pick up a very small amount of weight, less than a pound in all honesty. But he has no limit to how many things he can lift at once, each with that weight limit. He's been training with the big three and has found how to fly by grabbing every part of his body, how to throw heavy things the same way. It's quite impressive. Oh, and here comes the young man's friend."
"The boy with the weak hardening quirk?" All might watched as young Kirishima fought against Testutetsu from 1-B, the other boy's steal fist cracking upon impact with Kirishima's hardened form.
"He trained and made his hardening limit better." Nezu smirked "Amazing what happens when nepotism doesn't get in the way."