Can you say 'oversimplified'? Cost of living is not due solely to lack of affordable housing. EVERYTHING has risen dramatically since 2019 (one chart I saw with normal, everyday grocery items being compared showed ~50% increase in cost for every item). Wages have not increased 50% in 5 years. So, cost of living has risen across the board, wages have risen more slowly so the Americans who were just getting by or perhaps saving just a bit are now barely treading water or going in the hole (HH credit card debt at all-time high: > $1.3T bears testament). Housing definitely plays a part but it's not the only factor.
As far as 'solving' the housing problem, good luck. Builders are having to pay their workers much higher wages, construction material has risen dramatically and demand is far outpacing supply. There's not enough profit in building 1500 sq ft houses and selling them for $275k so good luck convincing builders to do so. Far more profitable building 2200 sq ft homes that sell for $475k and $475k is out of the question for most young people and far too many others, also, especially with mortgage rates right at 7%.