Not quite.

Free markets don’t instantly respond to changes in demand, but they do respond to price signaling. The fact that the number of nurses isn’t increasing dramatically suggests the market is reasonably happy with their numbers.

I'm not quite sure what you are trying to say. Wouldn't whatever you are talking about also apply the the number of homes?

NYC’s housing issues can’t get solved by people trying to toss money and manpower at the problem if the city doesn’t let them. Regulate away the free market and you don’t get to blame the free market for the resulting failures.