> Matching the approproate monthly payment is all that matters.

I'm not sure you follow. Monthly payment, assuming the same loan term and the buyer not losing equity, is (amount borrowed + interest) / term. If the person selling their house was paying a lower rate and their house gained in value, and the house they are buying is worth the same (as the housing market got broadly more expensive) but the interest rate is higher, it means that to match the monthly payment one would have to buy a 'cheaper' house than their current. That just isn't favorable.