It’s going to be very difficult to make housing more affordable with high interest rates and high inflation. I highly doubt just increasing supply is going to be enough.
limitations on what people can buy aren't popular but forcing housing to be owned by local people, who have a stake in the local community, rather than an REIT with investors 5 states away that are only interested in returns, or even an overseas owner. Taxing rental income harshly and the gains from the sale of housing would also contribute to making investment property less attractive, though there are second order effects to consider.
still, I think building more really is what's needed, so subsidies for building would be a great way to stimulate building, as well as better funding for city permit departments, and also challenges to more egregious zoning restrictions.
If housing prices drop and a crisis ensues, government/central banks lower interest rates and provide stimulus in the form of grants/loans/monetary expansion to prop them up. It becomes clear that the only way to make housing affordable is for authorities to have the political courage to let a crash happen.
Its just that never before has there been an investment firm large enough to take a big enough share of the largest market in the world, the US housing market.
The moment the federal government (Federal Reserve), private equity and investment firms like BlackRock started buying up every available home not nailed down it was the beginning of the end for the US consumer.