Here's the problem with this kind of an argument: how much of the success of the Leafs, Lightning and Capitals is attributable to analytics and how much of it is attributable to structural items that were in place or would have naturally evolved in the absence of analytics? Hell, the Sharks have purportedly been at the forefront of analytics for years now; it [somewhat] arguably has helped them at the draft table, but they're still waiting on that first Cup to come to town.
No one knows, which is why it's easy [and lazy] to attribute successes to analytics and failures to other stuff. The Blackhawks were loaded with talent, but purportedly got "over the top" with analytics. Really, was that the missing piece? Or was it the fact that they had a massive wad of talent up and down that roster and Quenneville stopped outcoaching himself in the postseason? We don't know, and we probably won't ever know - but the Blackhawks won 3 Cups, and they had won 0 before they started using analytics, so ... analytics helped us win 3 Cups!
And as pointed out elsewhere, analytics are not supposed to be the be-all, end-all answer to everything. They're supposed to help you identify trends or anomalies to consider ... but they're also supposed to be put into context with reality. Too many people [and teams] want to do the former as a rote application, especially based off of limited data that is treated as fully credible when in reality it probably barely scratches the surface of usefulness. [See: Dellow and his time in Edmonton and how purportedly roster and game decisions were made based off of well teh analytics says _____, it can't possibly be wrong!] Even worse, too many people [and teams] never monitor the results to see if things are changing - and if so, why. It's just analytics said this, and we're desperate for improvement, so why the hell not?
Don't get me wrong, as someone who did some of this stuff a while back I get the appeal of analytics. I also understand its limitations and can tell you where the analytics movement should be focused but isn't, and probably won't be for at least another 7-10 years because no one is even thinking about certain things.[Major spoiler: anyone ever discuss efficiency in terms of shots, puck possession, faceoff wins, scoring chances, etc.? No? There's all kinds of value there waiting to be unlocked - far more than Corsi/Fenwick/PDO/zone starts/whatever the current flavor of the day is in the analytics world.] But I would never claim that analytics gets a team from "OK" to "great" by itself, or even in large part. There's far more items typically going on when a team is bad that make it better than simply the implementation of analytics.