Perif, here's your list of Top 10 in wins all-time, I'm sure you wouldn't want many of these either:
Scotty Bowman
Joel Quenneville
Barry Trotz
Ken Hitchcock
Al Arbour
Lindy Ruff
Paul Maurice
Alain Vigneault
Peter Laviolette
Mike Babcock
As great as BT is, he missed the playoffs 7 times in 14 years with Nashville, and NEVER got to the 3rd round there. In Washington he won a Cup and lost in the first round the other three years and we know what he did with us.
Let's not kid ourselves here . . . he's not a Bowman or an Arbour or even a Quenneville, who does have 3 Cups and only missed the playoffs TWICE in 24 years.
I appreciate the argument as it's one that needs to be fleshed out, but you didn't flesh it out nearly enough. Let's look at it in detail...
Scotty Bowman who's widely considered the best coach of all time...
...Won 5 Cups with the Canadiens and had a .744 winning %
...Won zero with the Sabres and had a 594 winning %
Did Bowman forget how to coach when he went from Montreal in 78-79 to Buffalo in 79-80...Or perhaps going from coaching players like LaFleur, Robinson, Lemaire, Shutt, Gainey, and freaking Ken Dryden to guys like Perreault, Smith Gare, Seiling, and Ramsey might've had something to do with it?
The point is in order to compare coaches you need to compare how they'd do with the same ownership/organization and the same group of players. Of course that's impossible to make happen, but that's the prism from which the argument must be attempted to be had.
To wit, look at this insane group of players Joel Quenneville was "lucky" enough to coach in the past 25+ years:
Turgeon
MacInnis
Sakic
Tanguay
Pronger
Demitra
Hull
Courtnall
Duchesne
Hejduk
Blake
Theodore
Kane
Keith
Toews
Sharp
Seabrook
Barkov
Huberdeau
Ekblad
...And that isn't all of them. From St. Louis to Colorado to Chicago to Florida he's been working with hall of famers at every stop of his coaching career. Quenneville never had to deal with a roster close to the talent-level of the 2018-2022 New York Islanders. Might that have something to do with the level of success he's had? You bet your ass it does.
At the same time you referenced Trotz with Nashville who had "top scorers" like Ronning, Legwand, and Scott Walker. Even in their most successful years the top guys were Kostitsyn, Erat, and Hornqvist. The talent definitely improved when he got to Washington, but so did their team which ultimately lead to a Cup. And notice how the Caps have been since Trotz left...
At the same time there have been some very lackluster coaches that have won the Cup recently. Berube, Sullian, Bylsma, Carlyle, and Hartley are a few names, but again in each case look a the level of talent that they had to work with (and Berube was the benefit of the greatest goalie performance in the past 20 years).
And I don't think we need to discuss Al Arbour (whom I truly love). Something tells me you are familiar with the players he coached, the years each arrived, and how the success followed.
So the question to ask is...Which coach(es) could've had the same success with the 2018-2021 New York Islanders that Barry Trotz did? I don't think it's many as his defensive style perfectly matched the fact that they were a low-scoring team devoid of the top talent other coaches had.
The point is that the more talent you have on your roster, the less you need to lean on your coach to have success and certainly vice versa. And I'd make the argument that, between his stops at Nashville and the Islanders, very few coaches on the "best" of all time list got more results with less talent than Trotz did.