Way to hyperbole. You want your captain to be able to lead the team back when they get down, obviously anyone can do it and you appreciate it from everyone, but the people with the letters are usually the best at doing it.
How many hockey games, over the past 5 years, has a team won
because they were down and their captain gave some heroic speech? A game that they otherwise would have lost without someone to "lead the team back"?
Leadership doesn't win games. It doesn't score or prevent goals. It doesn't cover up for mistakes and it doesn't cause mistakes on the other team.
It's a nice feel-good idea to believe that willpower and mental strength can have an effect - we're part of the generation that is told "you can do anything you put your mind to", but talent, preparation, practice, and execution have roughly a billion times more of an impact on hockey games.
If you think that professional athletes can't suffer from psychological hurdles on the ice, you're underestimating the human condition.
If you think that professional athletes with a special letter on their jersey can have a notable and positive impact on psychological hurdles other professional athletes have, to the point where it affects the outcome of a game, I think you're overestimating the frailty of the human condition.