I'm thinking of something like Pale carnations with my idea.Not really the whole game, it often creates inconsistencies and illogical behavior in the "common scenes", and in general I find this a rather bland experience. It's easier for the dev yes, but that's it.
I think it's ok to do that for a while, but at some point you need several branches. It can be rather late in the story, past half the game, that would be the middle ground: not as hard to implement, but still giving the player the feeling his choices have real/permanent consequences. It's a difficult balance I guess.
You have a main story, and sevedral character stories. You can influence their results and behavior, but the overarching story will always be the same. Just which scenes you see and which endings you get will differ.
But this way you at least get some content every update, even if it isn't with your favorite girl.