Housing starts plunged during the Great Recession, and recovered to only mediocre levels. However, over that time the population continued to grow.
We fundamentally have a housing shortage, particularly in places people want to live. One massive problem is that it’s currently quite difficult to build net-new housing in places people want to live, due to a combination of overly-restrictive zoning and NIMBYs who ate empowered to block new projects.
The problem is particularly bad in popular urban areas. Either you build outwards or you build upwards. But if someone wants to live “in Boston”, “in NYC”, etc, they probably don’t want to live in a new build an hour’s drive away from the city in traffic. And infill development is generally highly regulated.
Adding a price ceiling without fixing the underlying shortage is going to benefit the people currently living in an area, but it will make it harder to find a new unit. Adding units isn’t the only important thing, but it’s pretty important.