I do see one problem with this type of regulation -- if you say "no more than 3 homes per entity", the "homes 4 rent" megalandlords will just create thousands of "homes 4 rent asdf" shell companies to get around the limit. I foresee tons of cat-and-mouse accounting shenanigans trying to dodge this sort of requirement.

A simpler method would be to increase both the property taxes and the homestead exemption, tuned so that individual homeowner pays about the same.

Limiting Airbnbs would help, too. Require city or county licensing for all guest accommodations, maybe, and have a set number of licenses?

Also, I don't want to try to kill off all housing rentals. Think about college housing, about people moving halfway across the country for a job, people who've just gotten divorced... there are lots of circumstances where it makes more sense to rent for a time than to pony up $$$ to buy a house or a condo. In a functional market, this would be, say, 10% of housing, and you wouldn't have the absurdity of "I pay $3000 in rent because the bank doesn't think I'll pay a $2000 mortgage".