I think you make a basic assumption that supply and demand make housing prices increase. This is not entirely accurate. 'Surplus-value' or capital is stored in housing. It is the storage of capital in spaces in cities that create capital and raise housing prices.

There are a lot of empty apartments in skyscrapers in New York city that the rich keep just as an investment. In the San Francisco bay area Chinese investors have bought up a lot of houses and just leave them empty. I think the problem of speculative investment and using property to store and build wealth is more of a problem than 'rent-seeking'.

If 'rent-seeking' is truly the problem the simple solution is to abolish the individual ownership of land, and instead have renters collectively own their buildings. This would be the socialist solution. I think this has been done in Europe with co-housing units.