Every other reason for why housing prices are climbing so much is at best a `yes-and`.
Housing starts per capital have been trending slightly downward since the 60's. Recessions have cut house construction harder, deeper, and for longer than in the past. The net result is an increase in prices, except after 2008. Housing construction was tanked to the lowest amount on record and has taken 10+ years to get back to historic levels. We're missing 10 years of housing construction at a national scale.
The is exacerbated in major cities which have severely restriction new housing construction both by imposing direct housing caps and onerous new construction taxes, and indirectly by changing the building code. California requires housing to have solar panels, that is a $15000 cost that new buyers must pay that older owners don't have to pay. LA wants to ban wood construction, the most accessible, carbon neutral housing construction option out there.
If you want housing to be affordable, you need to increase housing production by 50% and keep it there for years.