Its good for cheaper housing bad for house prices. Reason being that most houses prices are driven by ability to make house payments. At 4% rates you can afford to buy significantly more house than say 8% because a fixed payment of 2k a month pays for a 600k house at 4% but only a 300k house at 8. Lowering rates naturally drove house prices to the moon, raising rates will slowly cause them to come back to earth. How does inflation affect housing? Cause I'm asking for a friend . . .
a 2k a month payment at 8% for 30 years gets you a $275k loan. a 2k a month payment at 4% for 30 years gets you a $420k loan. A 4% interest rate hike decreases your buying power by $145k, not $300k So you're not wrong in theory, but you're off by a factor of two in practice. Mortgage insurance, property taxes and all the rest complicate the issue further and eat further into the difference.
The numbers you use are a better estimate. I used really rough mental math and it came out to a larger error than I expected. Probably because I didn't account for principal payment. As you state the effect is probably additionally decreased due to insurance costs.