Well, not this exactly. I mean when you rent a property, you're renting it from someone else who owns it. That's what residential property is. So there's really only three broad alternatives here:
1. It's owned by governments at some level. I think we can all agree this would largely be a disaster at any sort of scale;
2. They're owned privately. This could be by individuals or a corporation or a cooperative of some sort; or
3. There is no rental market.
Now as I mentioned in another comment: I do support not having unfettered use of residential property as an investment vehicle but you also need private ownership.
Personally I think a good start would be that the beneficial owner of any property is a resident of that city or state and if they're not, they get charged _much_ higher property tax.
You'll note I said "beneficial owner" there too. You want to hide behind an LLC or corporation to own your property without declaring your ownership? Fine. Pay for that privilege.
Cities should be by and for the residents in them, not hedge funds.
There are a couple of corner cases worth mentioning:
1. Rental buildings (ie not condos) should probably be treated differently than, say, individual units; and
2. I firmly believe that every mobile home park in the country should be able to forcibly purchase the land they're on as a cooperative from the current owner at fair market value. Hedge funds buying up the land mobile homes are on is really a disgusting form of capitalism, preying on some of the most vulnerable.