Can't they just progressively tax each house a person (or company) owns?
So your first house has very low taxes, because you need a place to live.
But of you own a second house, it's taxed a little higher. A third house is taxed even more, a 4th house even more than that, and so on.
That way more people can afford a first house but if they want to keep using homes as income properties then at some point it no longer makes economic sense.
You wouldn't have people trying to own 50 houses, nor would you have big corporations buying thousands of homes and driving up the prices.
What would be the drawback?