There is no right or wrong way to play this game. We all play it differently, and that's the beauty of a game like this.
To answer your question: I don't think all households/saves have to be multi-generational. I've had several stories where the story goal has been reached, and I moved on. It took me a long time to come to this realization though. I thought every single household I played had to be multiple generations or I somehow failed. Some stories are meant to have an ending.
Just like in real life, we have chapters in our lives that eventually get resolved. For example, the biggest "crisis" in your teens tends to look silly and trivial when you're in your 30s. That's the way I look at certain stories in my sims' lives. I'm playing a chapter of their lives, once that chapter is resolved, I move on. I hope that makes sense.