Exactly, by the time a hockey player has made the NHL, he's played for at least 18-24 head coaches moving up through competitive minor hockey, major junior, and/or college ranks. They have played all of the 'hockey systems' out there IMHO.
Adjusting to a new coach is simply adjusting to the new coach and his specific hockey jargon. 'Hockey systems' often have different names, however the actual tactics and methods are nearly identical.
Sure, each head coach has his preferences for player positioning and responsibilities within their version of the system. A seasoned NHL hockey player, and even NHL rookies, should be able to adjust to a new coach and his system nuances relatively quickly.
As a minor league coach, I coached players one season and then coached them again a couple of seasons later. They didn't forget how I wanted them to play within my systems despite being coached by 2 different coaches in between.
What I experienced was that some players decided they wanted to play my systems their way. Of course it didn't always work out because of this.
I think our Leafs, especially our core, have decided that they want to play their game their way and not what the coaches are asking of them. This happened to Babcock, Keefe, and now Berube.
Pond hockey only works if the opposing team wants to play that way too. Run and gun only works if the opposing team wants to play that game too.
IMHO, our core players are running the show. As long as they continue to do this, the longer we'll see the exact same results despite the coaches behind the bench and the coaches running the practice sessions.
JMHO.