Counterpoint: they're playing like they haven't given up on each other.
I don’t see it. If we were to argue that they haven’t quit on each other but quit on the coach, I’d apply that more to the end of Johnston’s time than now. They were playing miserable hockey and doing everything to not get scored on while occasionally creating offense but it was clearly over if they had to score much and they knew it. This team isn’t sulking or looking like they hate it all, they’re making dumb mistakes and having defensive breakdowns. They don’t even look frustrated or (mentally) fragile. That’s just not quitting in general; on the coach or each other. He was able to calm them down and get them refocused during a timeout in the first Rangers game.
Either way I’d be hesitant to because it implies every time a team quits on a coach they’re quitting on each other and I don’t think a coaching change would regularly fix that kind of issue. What I’d also argue was that they quit on the coach and each other under Bylsma. The locker room had been a mess for years under him and Shero which trickled out over the years. This isn’t that either.
Sullivan might not be able to get them to another cup if they even have it in them because there’s always a shelf life and bad habits inevitably catch up with coaches and GMs. Being too comfortable alone can cause issues, imo. I don’t think the team quitting on him will be the straw that breaks the camel’s back, though. Not after last season and now, the time that could have happened was likely in Kessel’s last season here.