Because Braxiatel would take it for his collection. I have no doubt of this fact.
The Doctor took one more look at the painting as the content smile on his face morphed into joyful determination. He was going home.
A thousand ideas of where to start looking were already running through his mind as he turned to push open the TARDIS doors.
"Oh dear," a suave voice called a screeching halt to his train of thought, "No one was supposed to be in here right now."
The Doctor's head spun so quickly he gave himself whiplash that he promptly ignored. He then stared into eyes so familiar he nearly cried out. The eyes blinked, recognition sparking, and after a moment the Doctor uttered a single word.
"… Braxiatel?"
One immaculate eyebrow rose, "Doctor."
"But… I… You! How can you-? I don't-!"
One side of a dignified mustache twitched slightly in annoyance, and Braxiatel rolled his eyes before interrupting the incomprehensible babble, "Well, this has been nice catching up Doctor, but I'm afraid I'm on a schedule."
The Doctor sputtered helplessly as Braxiatel passed by him pulling a stasis cube out of his pocket and proceeded to steal the Gallifrey Falls No More painting.
"What's taking so long?" Clara voiced from the now open doors of the TARDIS, "Is he another one of you?"
"I take offense to that," Braxiatel answered lightly, "My, my, Doctor, they do keep getting younger don't they?" the Doctor's face morphed into something akin to defensiveness but before he could say anything he was cut off again, "Well, I'm done here. It was a pleasure."
Only after Braxiatel had gone did the Doctor find his voice, "Braxiatel! You can't just steal these things!"
Clara watched with amused eyes, half wondering if they should go after the theif, but the Doctor didn't seem too worried about it so she asked the other question, "So… Braxiatel? Who was that then?"
"My thieving, idiotic, patronizing bro-"
"NO!" the curator had come back to find the empty wall.
In place of the painting was a little yellow sticky note with the words 'On loan to the Braxiatel Collection'.
No! You cannot actually say they are brothers! The audience is listening! Braxiatel is one of my favorites. Ever.
Inspiration for this ficlet came from a text post on tumblr (a link to which I will happily provide upon request) that wonders about what Braxiatel would do when faced with the Gallifrey Falls No More painting.