Unless you're proposing the government operates a People's Barracks, then housing must be able to make a return for someone or there won't be any liquidity. Which will mean that renters will be just as immobile; they'll have no way to rent a new place at their destination.
This doesn't require a People's Barracks. It could be done privately, merely by introducing a layer of indirection between individuals and housing stock.
I see a few problems with this idea. First, given the opportunity to behave more rationally, will most people act on it? Second, it doesn't fully decouple "home" from a physical place. It doesn't address the social environment of family and friends, or the costs of moving one's belongings. My other worry is acknowledged in the article but sort of dismissed: "homeownership has some social benefits—a higher level of civic engagement is one."
But what were people supposed to do differently?
Don't know if a good solution exists... housing is a very messy optimization process because people want vastly different things in their homes. I guess you could focus on niche groups so you can get some standardization going.