@Account Closed, thanks for the clarification! I think I get it. Let's see if I do:
I believe I took your first comment out of context and that's where the confusion was. If you were calculating cap rate on a property you were looking to buy given a certain price, considering a higher rent would mean a better cap rate, wouldn't it? If you buy a home for 100,000 and NOI is 10,000 when you first get it (cap rate of 10%), but raise the rent to get an NOI of 11,000, what you really got is an 11 cap, is it not? Sure, maybe you raised the value of the property by raising the rent, but the calculation for this cap rate should include the purchase price and not the value of the house, right?
Are we potentially trying to use cap rate to measure something that isn't necessarily valuable? Is cap rate only used to capture NOI and value at the time of purchase and past that, doesn't mean anything until you sell it? I think I can see why you would say cap rate is the constant. I believe it is driven by the area's market, so if you increase NOI after purchasing, when you go to sell it, you would sell for the same or a similar cap rate (that is acceptable for your area) but your price could go up with the NOI.
Sorry for rambling, this is my humble attempt to understand!