> But since the total lifetime spend on a house is absolutely lower if the interest rate over the life of the loan is lower, then it's true that lower interest rates make homes cheaper over their lifetimes.

House prices are determined to a large extent by interest rates [1]. People have a certain amount they are willing to spend on a mortgage payment each month. If rates are lower, that amount buys a bigger mortgage, so house prices are higher.

[1] https://www.bankofengland.co.uk/-/media/boe/files/working-pa...