I'm sure there are major issues with that idea as well, such as creating a rigid structure of sale and rental.

For example here, politicians made it very difficult to get kicked out if you rent a place for more than 2 years. You basically have to agree to move out. All that did is make virtually all landlords only lease for 2 years because it's hard to get rid of a bad tenant after that. It's a great thing if you can get it, but it sucks to have to move that often.

If you limit the % property for rent in a city, maybe companies will build turbo shit apartments (or extremely expensive apartments) for sale, and decent apartments for rent. The monkey paw is strong.