There's no more tradition or rivalry in the NFL. All the proof you needed was Tashard Choice getting Mike Vick's autograph a while back. Every player in the league is basically a mercenary.
That's not really true. First, Tashard Choice is a nobody, and most players are merely usuable commodities. The elite players in the league very much wear their colors with a chip on their shoulders for many teams. Plus, it's about bitter fan-base emotion steeped in bad-blooded NFL history. There's a lot of real butthurt and red meat between many of them.
Baseball and basketball have very little of this. There's a few decent rivalries, but it's not the same as football because of the physicality and gladiator nature of the game.
And players in the NFL do get caught up in it, at least temporarily. The Commanders, Giants and Eagles players genuinely hate the Cowboy organization. The Baltimore-Pittsburgh thing is real. So is the Jets-Patriots, Packers-Bears, Raiders-Broncos-Chiefs, 49ers-Seahawks, etc.
I agree with you when it comes to baseball entirely, and basketball for the most part as well. Soccer has suffered, too, although the fan bases are as emotionally invested as the NFL.