[AnthonyMouse]

But this is just assuming the conclusion. Suppose that you were to increase the housing supply as much as, or more than, the increase in population. The existing lower-wage workers don't have to leave until prices have already increased to price them out, so their leaving can't have been the cause of the higher prices but rather its effect.

So it's a feedback loop, but one which is prevented by keeping supply enough to meet demand, because then lower paid workers aren't priced out and cost of living doesn't increase.