I think this is an important point since the cost of money is a big part of building and buying housing. There are other nuances contained in this exchange too.

But beyond cost of money what, if any, specific argument are you making regarding housing? Lower subsidies in hopes the market follows? Further restrict the money supply to try and contain inflation? There are lots of second order effects that are too broad here, like high interest rates acting as a de facto subsidy to the wealthy (who then, maybe, buy more real estate, etc...