I like Sullivan, and certainly would be fine if he was the Rangers coach.
As for Gallant and Lav, again I agree as I have written numerous times. Gallant was let down by the players, Lav was let down by the players. The players whining about Gallant after last season was more telling about who they are, way more than my issues with Gallant. We are on the same page. I was not a Gallant fan, and was happy when he was fired, but it wasn't because the players whined or he way underachieved with the talent that is here, it was because I didn't think he was the right fit or really had a plan, structure, or strategy. I said many times, God could have been their coach last season, and they wouldn't have won. That was my opinion, not that the players were so good, and Gallant was terrible. Your point, maybe Drury should have done something with the players last summer is the point I think, way more so than if he kept Gallant or hired Lav instead. It is the players not the multiple coaches.
You have created this very strange thing where it was Gallant vs. Lav, and you have been doing it since the second Lav was hired. It is 100% your right and prerogative to do it and prefer Gallant and maybe be a little angry he was fired, but it is what you have done. I happen to think it is inconsistent, it was the whiny players under Gallant, but essentially with the same players it's Lav this time, objectively that is inconsistent. Even in the very simple way of looking at, Lav made it just as far as Gallant did, so I am not sure how that makes them any different no matter how you slice it.
The whole Lav didn't change things narrative is odd to me, he played different lineups and lines just about every game over the last 10 or so playoff games. That fact doesn't matter though I guess because he didn't put Laf and Trouba on PP1. I am also confused by the Lav went all out for the Pres trophy thinking, which I don't see as being true in any obvious way. It also ignores the fact they had 5 days off before game 1 against the Caps, 6 days off before game 1 against the Canes, and 5 days off before game 1 against the Panthers. I don't think rest or overworking them was an issue. It's like the NFL question, do you play your best players in the last game for home field or a better seed, some coaches say yes and do, other coaches say no and don't. I don't think Lav did anything over the top with the players down the stretch, and they had a ton of rest before and in the playoffs.
As for Trouba, the guy clearly was not close to himself when he came back from injury. Sure, he still hit and blocked shots, but he was beaten a lot, and took a lot of penalties. Once I found out he had a broken ankle, I give him a little pass though. I would expect he'll be back to his usual solid self-next season. Maybe not an $8M player, but certainly better than he was after the injury. Even with that being the case, I still go back to, if you keep Fox, does it make cap sense to have $8M Trouba on the 3rd pair, that is cap crunching Drury has to work through. You may be better off trading Trouba if you keep Fox, and he will be a 3rd pair guy