Well, the reason All Might stuck around is kinda spoilery, it's revealed in the last season. But it's also not really plot crucial. In the last season, we learn that Midoriya no longer really reveres All Might. He did when he was younger, but since he's inherited his power and made it his own, he now has his own goals and ideals. He still wants what All Might wanted, to be a Symbol of Peace, but there's more to it. He outright states that Uraraka is his hero because she's kind of an underdog and she fights for reasonable things, for personal goals. She goes above and beyond, but she isn't over the top like some of them (and not just Bakugo). Also, All Might reveals that Midoriya is his hero now, because Midoriya carries his own power. So, that's why All Might stuck around, he was genuinely concerned for Midoriya's advancement.

He was never really gonna make a comeback since he was getting worse and worse. He did, however, come back a little in a Batman or James Bond sense with a bunch of gear. It was cool to see but was a little extra and kind of unnecessary. So I stand by my assertion that Horikoshi should have killed him off.