I'd say that at no point in their history has the NFL had a more diehard fan base than they do now.
And just about every one of them to a man roots for a team first and foremost.
The question isn't if people root for a team FIRST.. its if the NFL didn't have the top athletes and best football players of any league in the world.. would fans continue watching, or would they go and watch the league that does have the top action.
Fans don't want to pay so much of their hard earned money to see mediocrity. You bring in NFL Europe players or UFL players to populate NFL teams and there simply won't be as much interest long term. Sure you may stick with your favorite team for a few seasons, but lets not act like everything doesn't really revolve around you wanting to see the biggest, strongest, fastest, most talented football players there are to offer. Its the reason the draft is such a huge event. Fans all across the world spend so much time with mock drafts, draft reviews and previews, etc.. everybody wants their favorite guys to go to their team. The best players. Same with the offseason. You want the best FA's, fans love the offseason in the NFL beacuse they get a chance to salivate over what potential new additions of players they can get for their football team.
Bottom line.. again.. if you bring in mediocre players to populate the NFL, the brand will lose value, and owners will lose money. If the NFL brought in slower, smaller, less athletic players.. we would definintely see (and could easily notice) a drastic regression or decline in the action every Sunday. The game just wouldn't have the same intensity and entertainment value if it wasn't played by the fastest, biggest, strongest, and most athletic.
Fans arn't going to shell out all that we do for game tickets, tv purchases, merchandise, etc.. for mediocrity.