So disallowing renting. So you don't control your property, which means you don't own it but lease it.
This is problematic, since not being able to open your house is worse than having difficulties with obtaining it. I agree that generally having some people own a lot of housing units is bad, but not being able to own a house means communism. And not as a scare, but quite literally, as in definition.
What about multiple of anything? How about 2 cars? After all, each car takes limited parking space and adds to traffic problems. How about eating more calories than one needs to live? Should we review all existing items that one can buy?