One thing I see being discussed is how high rates will reduce competition for homes (therefore lower prices). This isn't necessarily true for 2 reasons: 1) High rates mean higher finance rates for development/redevelopment projects, forcing new inventory to be priced higher to be viable 2) Owners with locked in rates (most homeowners) have little incentive to trade up, and more likely to trade down (increased competition for starter/smaller homes). Variable rate mortgages are a fraction of the mortgage market they used to be - this isn't 2008.
The only real solutions here are to radically rethink zoning at a city level, and potentially incentivize construction of affordable homes at a federal level through new lending programs.