I don't think housing is actually a bubble - a bubble is a situation that only exists due to widespread belief, but the current situation is fueled by real chronic problems. Namely: zoning laws that prohibit dense housing, and a widespread homeowner voting-base who vote to keep the laws as such.

The market can't adjust itself because it's not broken; everyone buys houses because it lets them avoid future rent hikes, and basically everyone needs to buy/rent a house near their job if they don't want to go broke, so there's a huge captive market.

A market cannot exist if the central government is guaranteeing loans (i.e. ensuring there are no survival incentives for lenders).

Remove the guarantees, and market will correct itself.