People should go find something else to invest their savings in.
You're going to need some exceptions. What happens when someone dies and leaves their house to their kids? What if someone's home is temporarily unlivable (say due to a fire or flood which requires extensive renovation) -- do they have to live on the streets?
And that's not even addressing the obvious question of what happens to tenants if there are no landlords.
The problem is supply, not distribution.
Keep in mind, about half of all adults are married, so each couple can own two properties. One to live in, one to rent.
I imagine we could figure out some way to handle inheritance, perhaps we could give somebody 12 months to decide which house the want to keep, and which to sell.
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.
I'd wager about 25-50% of the population prefers renting. Lots of people don't want to be tied down.