You are still assuming that rates will increase to that level.

Look at this. Interest rates haven't been as high as 12% since roughly 1987. That's more than 2 decades, and it's been almost 2 decades since 2008, where rates were already falling before the housing market crash. 2008 saw some of the lowest housing costs of the 21st century so far because of the amount of foreclosures. And yet, look at that, interest rates were around 6-7% and dropped to about 5%. Of note, the historical average is 7.70%, not the 12% you insist upon going back to.

Neither one of us know what the future holds, but taking modern economics into account shows that rates are unlikely to get high enough to have that make a meaningful difference.

Housing in the 70's and 80's wasn't cheap because of the interest rates. It was cheap because housing was rapidly expanding into suburbs, a suburbification. This is why rates could actually be that high, because the loans were comparatively smaller. You are confusing correlation and causation.

Look at this one:

Housing costs at 12% were not meaningfully cheaper. They were still slowly rising.