Why would anyone pay property tax if property rights stop being enforced? Unless you are actually just giving only the government property rights, allowing the writing and enforcement of evictions, which just makes the government the sole owner of all land the thus the new landlord. Even then, why pay tax when I can just go squat in anyone’s house or building while they aren’t home and it comes down to whoever is stronger getting to stay. Also no point paying tax if someone can just come take it from me. Unless you mean the police actually will enforce property rights for some people but just not others, which just means only those who can afford to employ the police have secure property while the poors just get to duke it out. Unless what you are actually saying is only don’t enforce property rights on secondary building ownership, and then only if that secondary building is not owned by a business that is not providing residential living space. Or are we also breaking up all multi-locatiln businesses the same way?
If everyone risks losing their home every time they leave for work or to get groceries, and only the strongest get to keep the best shelters, the social compact is broken and forming warring territorial clans and insular communities is the end result. Property rights are kind of a keystone for a functional society operating at a size larger than a rural village. It would cause less damage to just make owning more than a single family dwelling illegal, and force everyone to acquire a mortgage to wherever they currently live. This may partially lock your population to wherever they happen to live without finding someone to swap similarly valued dwelling units wherever you want to move to, but there are ways to lessen that impact. Alternatively, the government just seizes all property and doles it out according to whatever the government’s desires are for an area.