When people talk about how raising interest rates lowers the cost of housing what they really mean is that interest rates lower the value of income streams derived from monopolies and land is the biggest monopoly of them all. Monopolies basically can do perfect price discrimination, the more money you have, the more the monopolist can charge. Thus the obvious solution of giving people more money doesn't seem to work.

Raising interest rates is basically the opposite. What if we take everyone's money away? If people have less money the monopolists will charge lower prices. This didn't really solve the monopoly problem. After all, the monopoly allows perfect price discrimination. If the monopoly power is strong enough to get 30% of your salary it will always get 30% of your salary no matter how high it is. What really happened is that you now have less money to buy non monopoly goods.

Here are the practical implications: You can spend $1000 per month on your mortgage at 5% interest or -5% interest. The -5% interest house is significantly more expensive but the monthly payment is still the same. You still lose $1000 no matter what you do.