> How is the housing shortage not about the amount of available housing?

The name of the problem itself oversimplifies the problem space. There are lots of scenarios playing out today where there is ample housing and still a housing shortage. A major problem is that often the houses available do not match the ability of the renters to pay. So you can have lots of expensive houses being vacant, and lots of renters with nowhere to live, and have a housing shortage.

> Wages don’t need to increase if housing prices fall as a result of an increase in supply.

What? Yes they do! Wages are already too low to support a normal housing market, due to long-term wage suppression of the middle over many decades. Wages definitely need to rise for this problem to fix.