sure, and we see the effect of that because house prices are slowly going down now, yet just like mbs holdings, not nearly fast enough to put a meaningful dent in the covid gains. and yes, rates will go up, but a return to the free market is what we need long-term, instead of prices being artificially propped up by the government.
there's not going to be a radically free-er market in housing.
zoning regulations and the whole path dependence of the last centuries restrict choices to very few ones.
as long as the network effect of cities, the macro effects of the global economy (the dollar propped up, suppressing exports, which wreaks havoc on everything that's not finance) and various other factors (school districts, car dependence) have so oversized influence on where people can live.
and for the foreseeable future there are going to be very high-level coordination problems which keep the market in a pathological state.
https://fred.stlouisfed.org/series/CSUSHPINSA