I feel like a crux of the author's argument (and not deeply discussed), is the process where increasing population and density leads to higher wages for the highly educated.

We could imagine new companies moving to the area, with their complete team in tow. This creates a new opportunity for me to jump ship in return for a raise. My employer then has some incentive to 'steal' someone from elsewhere and may offer higher wages. The net result being little change, but higher wages for us both.

Is that enough to feed into the loop that keeps housing costs high?

Maybe the key step is the arrival of new employers, which bring the credit and wealth that soaks up the space created by any new housing. Some employers, and those employees not paid enough to keep up will choose to exit. But those spaces will be filled by the highly-motivated quickly. Meanwhile the relatively poor will continually suffer, there is nothing created that satisfies them.

So, dear leaders, build new housing but restrict employers, to make the bell curve that matches the people you want to populate your city.