This is the short term fix, and I completely agree with you.
The long term fix is, aside from letting local governments make minor regulatory changes to facilitate denser urban construction, to simply do nothing.
Cities are expensive. People will (and are) moving away from HCOL areas because of this. Businesses are adapting (e.g., with remote work) to hire people living in MCOL and LCOL areas. At the same time, new economic agglomerations are springing up in these areas to support growing populations.
Given enough time, two things will happen. Many of these MCOL and LCOL areas will become more expensive. Some will urbanize. Some wont. Second, eventually, people living in the areas that don't urbanize will realize that they actually would enjoy living in a HCOL area. And the cycle will continue.