He assumed that the payment is the same meaning the principal for the same house went down and so this is neutral. If your payment is the same it doesn't matter what is principal vs interest. In the best cases rates go down in the future and then you refinance and your payment goes way down.

House prices tend to be "sticky", so that assumption is probably wrong. People who own a house often cannot afford to sell for the current value since it won't pay off their loan and leave enough money left over for a replacement house so they avoid moving. Eventually things get bad enough that they "sell short", but that takes a credit hit so you don't want to do that until the loss is large (and in turn you gain more).