Well, in fairness, Lebron didn't "adjust" later on. He was dreadful against the Mavs and was just never dreadful again. Second is that Casey was the assistant in Dallas and not the coach. He built a defensive scheme that on autopilot with just okay defensive personnel was a top 10 defence, there's not a damn thing wrong with that. But when he was in the big chair, he showed a distinct inability to adapt and manage in game situations.
I think Babcock's reputation has largely come from his ability to get a lot of out just okay rosters. There's the cup and the internatonal success, which doesn't hurt his profile at all, but he's credited with getting a lot out of a middling group in Anaheim. Then he won with studs in Detroit, but the studs got old and went away, and Babcock's group remained competitive for longer than they probably should have (people were screaming about an impending rebuild in Detroit for years but they never fell apart, always made the playoffs regardless of what was on the ice). Then he came to Toronto, turned a group of misfit toys into about as good a team as they possibily could have been, and has developed every young player of note into impact guys since his arrival. He's not Pop or BB, but I don't think hockey has an analogue for those two. It's really hard to argue that Babcock isn't a top 3-5 coach in the NHL.
I see this era of NHL hockey as the last throws of the old guard, very similar to what 10 years ago was like in the NBA. Where there were still a lot of old guard coaches with huge reputations kicking around, who were more or less rejecting what the analytics were saying about how the NBA game was changing. Now? It's getting harder and harder for coaches to get or keep jobs without bowing down to the importance of space, ball movement, and 3 point shooting. We'll see NHL clubs do the same over the next 10 years imo. As a coach, you'll either buy in to the value of puck possession, shooting from high percentage areas, speed and skill, or you'll have a difficult time getting or keeping jobs.