I agree OP, I am not sure why so many people keep talking about rent, it's not really about kids moving out specifically, it's about kids becoming adult.
I think most kids go through a very strong streak of wanting to be independent at around age 15, which is also when they are typically most annoying to the rest of the family. I suspect this is the biological drive to separation and independence asserting itself. This is when kids should become more independent at school, get a job, and start to be significant contributors to the household. Not financially, necessarily, but their work should feel not just like "helping" but as if it is really part of making the household function and thrive.
So maybe that could be starting dinner after school, managing the yard work on weekends, taking a younger sibling on the bus to swimming class, or working at a job to earn their own spending money. What is possible will depend on the household and where people live, but the exact form isn't set in stone. It's about contributing to the common, not always being a recipient,
Most younger teens feel proud to help out and like the independence and responsibility. And once they have that, and maybe even are earning their own spending money, that is really motivating and empowering. In my experience parents see a lot of dividends in other parts of their kids lives. Of course they don't grow up immediately but there s a direction of travel.
And no, school work and clubs, for the most part, aren't quite the same, because they are usually still kids being a kind of recipient. (I will say this isn't set in stone, I've seen kids in a few activities like cadets really sprout general independence, but overall activities and hobbies don't seem to have the same effect.)
When kids are not feeling that kind of sense of contribution and independence by about 16, or even a bit before really, i think many become used to being recipients, it's like a bit of a developmental window is missed. They get used to the sense that they will be taken care of and that someone else is ultimately responsible for their well-being and that others need to take action to fulfil their needs.
It is a lot harder now for kids to get that independence overall at the right age - parents almost have to fight to allow those experiences to happen. Fight cultural expectations, among other things. And their own impulses to infantalise teens that are really capable of quite a lot. I do think it can be done though.