Earlier quoted context omitted.
Buy what? If rent were illegal, there would be far less housing because most people cannot (or will not) save enough capital to create or buy their own.
You need to challenge your assumptions more, why couldn't you just make single family dwellings illegal in high demand areas? And have the state in charge of housing? Unless you mean to argue about current laws and situations, the main point of these discussions and this post is that they are not working.
Putting the state in charge of housing is the cause of the existing problem. They become captured by landlords, or favor higher property values because they increase property tax revenues.
What you need is some constitutional restraint on local zoning rules.