Because the left thinks that the fix for housing shortage caused by governmental regulation starving the market of housing is for the government to intervene further and subsidize the thing they made unobtainable.
Speaking as someone who routinely votes for the most extreme crazy left-wing loon on the ballot in local elections (disappointing choice this time - only one, the "Trade Unionist and Socialist Coalition" party candidate), I'd much rather they did it by forcing the building of a lot more houses, but that seems less palatable to the rich than subsidies.