NASCAR made the mistake of believing it was a sport with national and not just regional/parochial appeal. That ultimately was their downfall. The NFL, to varying degrees, either is or is about to make the same mistake except it'll be with making changes to the sport to attract casual fans (think people who don't know much about football, but might tune in if they overheard that Tom Brady and Peyton Manning's teams were playing each other).
They took a race away or stopped racing altogether at some of the traditional, southern tracks where their core fanbase lives (granted, a lot of that had to do with bad attendance) in favor of racing out west or in the midwest. The constant rules changes are an absolute joke and have driven away longtime, traditional fans. Especially now that Dale Jr. is gone, the sport lacks a "good ole boy" type of driver. The most successful driver and face of the sport (Jimmie Johnson) has the charisma of a damp rag and personality-wise is the antithesis of someone like Dale Earnhardt or Richard Petty. As the sport grew, it really started to develop a corporate feel to it, which drives away the traditional, blue collar fans that make up their core fanbase.
The allegory would be if college football was only popular in the southeast, but people perceived a trend, so a bunch of northeastern and western schools start fielding teams and building 75,000 seat stadiums. The trend lasted for about 5 years before peaking.
NASCAR leadership is probably right when they say that the recession hurt them more than other sports, but to continue to use it as a reason for the decline in the sport is an excuse. They have structural and marketing/image problems that I'm not really sure are fixable, outside of returning to a purely or almost-purely regional sport like it used to be.
There also could be a generational component to it; millennials (yes, I know it sounds like I'm blaming everything on them) don't like cars as much as previous generations. Kids aren't busting down the door on their 16th birthday to get their driver's license anymore. They don't particularly care to drive and won't if they don't have to, much less actually work on an engine or something. Computers/smartphones are way cooler to them.
The NFL is a money printing business. I disagree with your assessment of it.