Two things.
First, remember that as you pay for the top 250, you already have less of an arguement. You have 230 channels that you don't watch, because you choose to pay for them to get the channels that you want, at least I hope. If not, then you are a TV junky who wants it all. I know people like that exist and some have posted on Sat Guys. You are taking this from your position as a "non-music fan" who chooses to pay for everything, except premium services. I know why you might, as I paid for that package to get The Movie Channel and Encore. But, you need to look at it as if you were paying for the 120 package.
Second, this notion that non-sports fans are entitled for a consideration over your plight is obsurd. That argument of apples and oranges is exactly why I'm willing to bet that we would be like rams if we were to be discussing more important matters over in the Pit. That music channel that you refer to, or reality channel (I'm leaving out the shopping channels. You don't pay to have those.) is costing less money per sub, and has less penertration, as they mostly are in higher packages. Therefore, you have an option to not pay. The NFL is demanding viewership by all. Now, I can't prove this, as I'm tired and don't want to look it up, but I'm betting that the NFL Networks yearly viewership does not warrant what you refer to as the demand it claims that it is worth.
In essence, you are stating that because you, your families, and your friends watch it, then it's in high demand. It is in your microcosm of people, as it is in mine, but it isn't as widely as you think. The NFL as a league being in high demand doesn't automatically mean that the NFL Network is too. I can get my NFL live game fix through ESPN, CBS, FOX, NBC. I can get my talk about the NFL fix through all those, plus FOX Sports 1&2, NBC Sports Net, my local RSN, etc. Simplified, the NFL Network's product is diluted through so many mediums, and is so niche, that it is not in as high of a demand as you claim.