Fresh legs are overrated.
From the athlete's point of view, he is most effective when given the opportunity to play regularly. "Give me the damn ball", says Keyshawn, and he is right. Any star worth his salt wants to be the focus of his team, the player around whom the action is centered. Ask them, and they will tell you that regular playing time helps them to keep their focus, and stay in the flow of the game. Goaltenders in hockey sometimes have a hard time staying sharp if those first tests do not come until well into the halfway point of the game. And it seems from casual observation, that running back by committee as practiced in the NFL might help maintain the health of the players (not) involved, but it doesn't necessarily seem to translate into more success.
Continuity is necessary to become proficient at any repetitive task. Stopping pucks, tightening lugnuts, hitting the hole. While players practice on offdays to hone these skills, they will tell you that there is no substitute for real live game play, taking that first shot, stopping that first breakaway. Being switched in and out at the coach's or the management's discretion is a distraction, and it gets in the way of that continuity.
You might argue that rotating players is a motivational tool, used in an effort to make the competitors for playtime work harder, give more. On the other hand, you could also believe that using committees is an effort to placate the players involved, to rationalize the salaries paid or to satisfy egos. Ultimately, the decision is up to the coaching staff, and they will do what they think best to win. But because the decision is out of their hands, you cannot help but be just a bit sympathetic when a player says "give me the damn ball."