The main factor for people buying houses is the monthly payment. When interest rates go down, abstract asset prices go up to compensate. When interest rates go up, abstract asset prices go down. So your scenario of interest rates going up would actually enable people to do things like make a larger downpayment (rather than suffering the PMI trap), and make it reasonable to pay off a mortgage early.

But as I said, the change in interest rates is unlikely to be that large for secured credit like a mortgage, as the main thing guaranteeing the loan is the asset itself.