“… at some point in time, high rates will cycle down to lower rates and then you are in fat city as long as your home hasn’t depreciated to the point where you cannot refi.”
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If the relationship of housing prices to interest rates holds true, if you buy at a low price when rates are high, when rates cycle down, then housing prices will be up. At that point, you’ll really be in fat city because you’ll have 1) accumulated plenty of appreciation, and 2) the ability to refi at a lower rate = low carrying cost + plenty of equity.

After you refinance at a lower rate, if you then continue to make the same monthly payments as when the rates were high, your house will be paid-off much sooner.