But if I understand correctly I feel like the overall mindset of teams is to give the players the tools to succeed, then it’s on the player to see those things through. (Which in my eyes is mostly how it should be.)
Quite right. Because there's not enough time to do that kind of development during a regular NHL practice schedule. So if players are going to put in the hours needed, and to improve over how good these guys already are it's going to take countless hours, that kind of work happens on their own time.
This is how that kind of training looks in the off-season.
And it's worth pointing out, it requires a team of guys to help a single player with these skills. Look at all the help Crosby is getting. You need a compliment of skaters and goalies to be there if you're going to practice anything remotely resembling a game scenario. So it's not like you can just pop on down to the local rink in the off-season and get better at "puck control" without a fair amount of coordination and resources.
All of this is to say, so much depends on the individuals commitment and willingness to do this kind of work.
Now, should the Wings help set up this kind of environment? Absolutely. And I'd be stunned if they didn't. Because it's a god damn pro NHL team with freakin' Steve Yzerman, a guy who knows a little about hockey, running the show.