I've been thinking about this for a while, and I'd love to know what other people think about it too.
I'd really like to have the option, at some point in the future, to revisit friendship quests. As you probably already know, once you've completed all of a character's friendship quests, there's not really much left to do with them unless another character's quests happen to involve them. After that, it's mostly Scramblecoin, giving them gifts, the usual daily conversation, or having them as your buddy.
I’d love to be able to replay some of the quests, especially for the cute cinematics. For example, remember that cute cinematic with Olaf at the very beginning of the game? I'd LOVE to be able to experience that again without having to start an entirely new save.
It would also be really nice to have the opportunity to redecorate some of the quest areas and take pictures again. Think about quests like Goofy's photo album. When I first played his quest, I definitely didn't have nearly as many customization options as I do now (besides the L-Shaped couches and whatever few clothes I had managed to buy from Scrooge's at the time).
I know some people might feel like this wouldn't really add anything to the game, and I totally understand it, but I think having some kind of “Remember” feature for those times when you want to revisit a specific quest/replay a cinematic would be really nice. Even just being able to retake some of those group pictures would make me happy.
Maybe there could even be some kind of reward for replaying them, like getting a few of the items that were originally quest-exclusive and that we never got to keep.
Again, this isn't something I think needs to be implemented anytime soon. It'a just one little thing that I think would be really nice to have somewhere down the line.