Because housing is a vital human necessity, so much like healthcare, the price ceiling for it is effectively infinite, because almost no-one can reasonably opt-out of purchasing it. (And due to how it's financed, it's not even really capped by people's income, since all of society is built with the requirement that everyone spend more than they could afford, just to get basic essential housing)

Saying "new (for-profit rental) housing construction will fill the shortage" is like saying, "Yes, Nestle charges an obscene amount for our water, but if we just let Nestle pump more water from the ground, they'll voluntarily sell that water to us for less".