We have become so utterly focused on the specifics of lending rules and incentives, yet the biggest problem is more simple: there are not actually enough homes available to house all the people that want to buy a home to live in. There would be no housing crisis if we had a regulatory environment that encouraged the housing market to produce enough homes to actually meet demand, at prices people can afford.
That means smaller individual spaces (be they single family or multi-family buildings, built with vastly more automated processes, and streamlined permitting and approval processes.
It is mind-boggling that today that in a major city today in the US a working person should have to pay 30+ years of income just to afford a space to sleep.
Travel a little to actual first world countries and it is not hard to find places with far more sane balance of housing construction to population, with prices at far lower multiples of average income.