I have $100k invested right now, make $74k, and spend $37k. My savings rate is 50% as far as I'm concerned, even though I theoretically could withdraw $4k from my investments and spend it indefinitely. My withdrawal rate is currently 0%.
Based on your calculations, if I had $1,000,000,000 invested, my "savings rate" would be ($37,000+$40,000,000)/($74,000+$40,000,000)= 99.9% savings rate. Yet since I count the $40,000,000 as savings, that means it is being withdrawn and reinvested. So I could either say I have a 50% savings rate and 0% withdrawal rate, or a 99.9% savings rate and 4% withdrawal.
I understand what you're saying, but I don't understand why you'd ever care what your "savings rate" is when you're withdrawing from your investments. If it makes you feel good to brag about spending less than you could, that's fine, but I don't see any way it helps you analyze your situation. You're basically combining savings rate and withdrawal rate to make your savings rate look higher.