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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.