In the short term that's absolutely correct. In the medium term higher home prices and lower interest rates encourage more building. Assuming that NIMBYs don't

In the short term that's absolutely correct. In the medium term higher home prices and lower interest rates encourage more building. Assuming that NIMBYs don't prevent that construction (big if), that would lead to lower home prices. But high interest rates isn't making things affordable because first time buyers can't afford a mortgage at those rates.