"Just play for the love of the game."
"Win for pride."
"Play hard because you're competitive."
It's all hogwash. There's a reason tangible incentives and awards are offered for high performers in the real world. The vast majority of people don't perform well or work hard out of some internal sense of "pride" or "love of the activity." They do it because they want a raise, or a promotion, trophy, or some other tangible recognition.
Just because we're talking football here doesn't mean this desire for a tangible award for a job well done goes away. You take the award away, it's human nature to care a little less, no matter how subconsciously or subtlety, and that ambivalence will affect performance.