Anecdotally, the most successful competitors I have seen (in team based stuff) are the ones who are solid between the ears. A player who can think at a high level (not even just the game, but in general) will usually have a more successful and fruitful career ... being a good teammate, being able to break out of slumps, being able to show humility to improve your weak areas, acknowledging your shortcomings so you can improve upon them etc.
I think the big reason they went Slaf over Wright had to do with something between the ears. Slaf seems very charismatic in a way I never really got from Wright. One feels like they are speaking from their heart, and the other from the hockey handguide for talking to the press. The on-ice product is only one component of a player; and you can see that the most successful stars in the NHL are ones with robust personalities, otherworldly talent, or something in between. You really need that swagger but it needs to read as confidence as opposed to conceitedness, and I think while Slaf's reads as the former, Wright clearly rubbed people the wrong way.