I don’t think 99% of players care about rivalries and where the title goes anywhere near as much as fans. Players are selfish. Look at the bust up Chelsea had over that penalty.
For example, a Spurs/United forward will always care more about scoring and improving their own stats than playing a part in a Arsenal/City title win.
Players just aren't fans
Not real ones. They weren't given the chance to become real fans, they were too busy playing and becoming rich
Not destroying their bodies for 50 hours a week and have the only respite from that in their life football, memories of childhood, adolescence, pubs, fathers going the game
Players though we know they're passionate and some more than others, couldn't hope to be even 10% of what a fan feels