I think it would be nice if the world around your Sims changed as your Sims' household changed with it.
The closest thing to this sort of "story progression", without mods, is the interaction in which you can "Ask About" one Sim to another. This results in the two introducing themselves to each other later. The other option is to "Talk Up" a Sim to another, which in turn prompts them to begin dating one another later. Both interactions then notify you about how things went.
Though it's not much progression, it's a start at least?!? I just hope they build off it at some point. While I generally don't care too much about what other Sims are doing, as I'm focused on my Sims, I would really love to see the world change as my household changes. I think it would be really great if I could take my original Sim's great-great-grandchildren to the park and they play with Alexander Goth's grandchildren. It would feel... I dunno sweet? Nostalgic? It would just be really nice to have that kind of world. :3