Henry George liked this idea and these ideas were very present in Catholic Social thought.
We have a homestead exemption here in Ohio, but lots of people commit outright fraud and just claim they have multiple primary residences, complete with multiple primary mortgages. Then they rent the 2nd homes out.Double the property tax rate in the area and then grant a 50% "homestead exemption" for all those who actually live in their homes x-number of months per year. And then use the proceeds for affordable housing or some such.
One of the biggest distortions in the housing market isn't mom and pop landlords, but big finance buying up single family homes; according to some estimates, 100% of new home construction has been swallowed by large, institutional investors. In short, we are becoming a nation of renters and serfs.Locals who live in their own homes would be unaffected. Out-of-towners who are buying weekend homes or AirB&B type rentals would face a serious tax incentive to look elsewhere. Of course some ordinary people and landlords would be affected as well. It is very difficult to surgically tailor these sorts of measures to have the exact effect that you want without any spillover effects.
Big money controls big government, so I really don't see much hope this will be changing anytime soon. The end result is a debt bondage system for virtually all people, much like the debt bondage system in India. Nobody has the political will to do anything about it.