They're also mostly having low population growth compared to times when they weren't having a housing problem.

Housing problem comes from the job market. Cities with good jobs will attract people and the price of renting/buying will go as high as they can bear. Most of the benefit will go to landlords. Moving to a better job market will make you little benefit because your increased pay will be largely swallowed by the cost of housing.

The problem is that employers want their employees physically present at the office, and roads can only carry them so fast, so being closer to job opportunities will reflect on the housing cost. Maybe the solution would be to make workplaces more widespread, improve transportation to expand commute reach under 30-60 minutes, or support more remote work.