The children could have one each too, perhaps only once they reach 18.
I think there would be plenty of rental stock still.
Still, I'm more than cognizant that there must be huge exceptions carved out for any of these ideas.
it does make sense if you want to save a nice retirement home for yourself or a place where you want to raise your children while you work and live somewhere else.
it doesn't have to be a closed loop though. owners could be (and in my example most likely would be) renting an apartment/flat in the city which is not privately owned)
I'd wager about 25-50% of the population prefers renting. Lots of people don't want to be tied down.