[closeparen]

Scarcity really exists. Markets are one way of contending with scarcity; you could also use a lottery or a queue. But people who lose the lottery or get stuck in the queue are just as deprived as people who can't pay the market price. And there are exactly as many of them. Probably more, since there is no mechanism to bring more supply online when the queue is deep, while the market mechanism works to some extent, choked off as it is by government limits.

Fundamentally, the only way that more people can be satisfied with the housing they have access to is to produce more of the housing people want.