"would not a raise in interest rates see an accommodating lowering of pricing to maintain the sell-able monthly amount?"

Many buyers buy projecting past inflation into the future. If prices fall the rush to get in goes away. Also the person who has a current loan they can afford at x % APR is paying $ y per month. If rates jumped dramatically and they still owed money on their old loan they probably would not be able to get another loan for a similarly valued home...so they...