Everything else being equal, you almost always win when buying a house in inflationary times. Even if you pay a high initial rate you can always refinance to a lower one later. If rates stay higher for longer than anticipated your income is most likely rising as well. In either scenario your debt service expense is trending down as a percentage of your nominal income, and your asset is trending up with inflation.

But surely you notice that when interest rates go up and down, that movement is tied to changes in expectations of inflation?

The '80s homebuyer did great on their purchase, but not because borrowing at 20% was such a steal. They profited because their home subsequently went up in price faster than inflation did.