The private sector has no reason to build low income housing. If you factor in the cost of land, labor, and materials then there would be little ability to charge below market rates. Low income housing can really only be built by the state or city unless there is some magical developer who is willing to lower their profits.

The addition of newer units to the market should eventually lower the price of older ones. It may not be a perfect solution but it will still help.

Finally, to address how do we stop the “never-ending stream of wealthy people” moving here- we don’t. These people will continue to come here regardless of how much housing there is but if there aren’t enough newer/higher end units then they will opt for the older ones like they do now.