Horrible policy– I may be on "the left" but the objections of the economists are, in this case, entirely correct. In the end it ends up squeezing newcomers, young people, and middle-income people of all stripes, at least whenever it is applied for any longer than the briefest of band-aids (in concert with other, more durable approaches) that CrabCake envisions.
There are better, less discriminatory and capricious, ways to tackle displacement.
Also, huge misuses of real estate crop over time, since moving usually results in a massive rent increase. So the couple whose children are all grown stay in their massive 3 bedroom, while families with children sit on waiting lists.