Higher interest rates won’t change the calculation that much, since the expected appreciation (inflation) might also move in lockstep. I don’t think a 13% interest rate and 10% inflation is much different than a 6% interest and 3% inflation as far as the fair assessment of rent vs. buy. And probably, medium-term interest rates will be somewhat above medium-term inflation, as far as the latter can be forecast right.
I don’t see any cases where you would be completely off with your estimate.
Maybe in 1980 if you took a long-term loan at 17% and inflation dropped thereafter by 5-10%. But so did interest rates, and you could refinance.
Or maybe when recently the 10-year was at 3.5%, you might have a hard time guessing inflation. It probably wasn’t 1% but rather 5%. So you could have paid slightly more for a house, but there probably wasn’t one close to that price anyways.
So these rent vs. buy calculations are probably a good guide. I emphasize “guide”, because ultimately history might be more accurate. If history shows that mortgage/rent was typically between 0.9 and 1.3, any calculation won’t change the fact that 0.9 was a good deal, and 1.3 wasn’t.