They don't call coaches coaches for no reason...they do coach. They put together systems, decide on how the pp and pk should be played, put together lines, match lines with other teams lines, etc. To think that they just are there to motivate their players is short sighted.
A determining factor with any team, sports related or not, is to have cohesion as a whole. You need everyone to believe in what your goals are and how to accomplish them. Yes, a good portion of doing that is having a coach who can motivate your players to believe in them.
Some teams just don't have unity in them either, with cliques forming and what not, and no matter what coach you have behind the bench if the players aren't willing to work for their teammates all hope is lost. You take Chicago for example, they are all young, all growing up together, and are willing to fight next to the guy sitting next to them.
Have to agree with Robert, hard to motivate someone to play when they are making millions. But on the other hand, they wouldn't have gotten to where they are at if they didn't love the game to begin with...if they don't love the game they should hang up their skates...