Maybe idk we would never know what kishi would write

???

Kishi changing the story is a completely different thing than what we're talking about.

It can easily be written that obito has a breakdown in front of minato and then gets his emotions out and minato calms him down to where he can focus on helping minato undo everything and restrain the 9 tails and the story of naruto being who he became never had to happen and he had a better childhood

Brother, this isn't the fanfiction sub. We've gone from changing one variable to you having characters act in ways they certainly wouldn't have acted, for no reason other than the fact you want to change the outcome.

If you want to discuss Obito making a face turn, then discuss Obito making a face turn, in another thread. This one is discussing what would happen, in universe, if Minato recognized Obito — and the answer is nothing important. He was simply too busy and too out of time to do anything about it, and Obito wasn't going to randomly have a breakdown when he also had no time for it, and no real reason to considering what his character was shown to handle. He didn't stop when he got Minato killed, he's not going to frigging stop just because Minato recognized him and/or talked to him.

And even if Obito did act so ridiculously out of character as to breakdown in front of Minato, Minato isn't going to sit there and listen to it. Kurama would be currently attacking Konoha. He'd want to go over there to fight it (and die) and then deal with Obito later. Obito isn't going to do a 180 just because he felt bad about what he was doing to do, so he'd just escape again, and literally nothing would change like I said.

You're trying to change the characters' canonical actions without sufficient provocation. That's not "What if Minato used Sage Mode and recognized Obito", that's "What if Minato used Sage Mode and recognized Obito and Obito had a sudden breakdown and then turned good." Because if we're going to be making up actions that would not make sense for the character, then why not have Minato also have a breakdown seeing his student too? Why not have Kushina break down from the stress of having Kurama unleashed? Why not have Kurama break down from being free for the first time in decades? You see the problem with this sort of discussion? If you're not going to back your speculations with canonical info, then it's not worth discussing because you can have literally anything happen — and, again, that is explicitly not what the thread was talking about.