I think the concern is that:

• The rich would try to skirt this with numbered or shell companies, or family or other relations.
• The rich would pass this onto tenants.

Now, the solution is to a) couple this with rent control, b) exempt purpose-built rentals from this endeavour, and c) punish serial transgressions with confiscation.

Frankly, I think the idea of punishing malfeasance by landlords with confiscation to be just awesome: if you're a predatory slumlord, we take the house and repurpose it as RGI public housing. Do I worry about the government becoming predatory? Yes, yes I do, but in this case it's a lesser-of-two-evils thin.