John Tortorella has run multiple stars out of Columbus and has had borderline no success with the Jackets outside of their upset against the Lightning in 2019. John Cooper was on the hot seat in the eyes of fans because of how many times the Lightning had lost in the playoffs without winning (especially after getting swept by the Jackets in 2019), and he had a track record of making baffling lineup decisions such as playing a recently bought out Dan Girardi in a fringe top-4 D role. Babcock continuously played scrub grinders like Glendening in highly elevated roles, plus he was generally a piece of shit person (such as that story with Kadri and Marner). He also was head coach for Canada for 2 gold medals and made it to 3 cup finals, winning 1 of them. Dan Bylsma is in basically the same category as Babcock minus being a piece of shit.
You can extend this to GMs, too. Steve Yzerman is considered one of the best GMs in hockey. He also ran Marty St. Louis out of town while in Tampa Bay by not putting him on Team Canada's Olympic team and has never won a cup. Joe Sakic was considered a massive failure as a GM early in his tenure, with the Avs being a historically bad team and calls of him being as bad of a GM as Roy was a coach. Now he's hailed as one of the best GMs in hockey.
The point I'm making here is that you can point out "that many blatantly obvious flaws" with literally any hockey coach, GM or any other executive position. If badly losing 2 playoff rounds and having dumb personal feuds with a few players counts as "that many blatantly obvious flaws", there are 31 head coaches in the NHL that have "that many blatantly obvious flaws". If the amount of flaws that Sullivan has rises to the level of "fireable offenses", there wouldn't be a single coach that would last more than 3 years with any given team.
This isn't even a defense of Sullivan here, like I said above I want him fired if they flame out in the playoffs this year. This is a criticism of people who attack him and completely lack nuance and perspective in that discussion.