Well, that's kind of the point - if the possibility to live in a particular place is scarce and so desirable that it costs $4000/month, then you either can afford that or don't live in that place - and this mechanism is useful; it allows people who really value living in that particular spot to pay the premium and do so; and the money flowing in provides a strong incentive to increase supply.

If Grandma needs subsidized housing, that is something that should be separately agreed upon and implemented, presumably from tax revenue. The idea of forcing landlords to pay that subsidy basically at random seems ridiculous to me, the kind of thing that results in discrimination and legal fights.

Part of the problem with talking about some policies is differing visibilities of suffering. Yes, the old grandma who has lived in the same apartment for 50 years has very visible suffering if you make her apartment market rate. However, what about the people who were never able to move to NY to start their career and family because of the policy? Or a family that had to leave the city and everyone they knew because they couldn't afford it, and the grandma monopolized all of the 'affordable housing' benefit?