So I'm not sure how much I can offer here, but to your question of 'what does organized sport have against Pete Carroll?' I'd venture to say that it's an issue of him being a rebel, playing culture-wise (baseball 'purists' STILL complain about contemporary bullpen usage, even though it's clearly the superior methodology compared to letting the starter face the lineup four or five times a night); a renegade tactician who, like Billy Beane, only wants to get the job done and is fine with doing it in an ~ugly fashion on a shoestring budget (or with year-in, year-out, league-leading UDFA density on the roster); and, finally, that he IS charismatic and therefore seriously dangerous to the Establishment.
Billy Beane was sneered at (still is?) by many in baseball, but it rarely went beyond that because tactically speaking he's got inferior terrain (a club based in Oakland, regardless of how well-run, can NEVER compete with one based in a major metroplex on a long-term basis). If he had been in charge of a team like, say, the Mariners back in the early aughts when they were top 10 in payroll, I think the systemic pushback would have been far, FAR worse than it was with him in Oakland. But since he, unlike Carroll, wasn't overly 'charismatic' or 'influential' culturally within the game, the pushback was less (blatant) than it is for a guy like Carroll.
Nobody really likes change--especially not the people who have benefited from the status quo. I think Pete Carroll represents existential threats to the status quo wherever he goes. That's how the world treats revolutionaries and trend-setters: a mixture of revulsion and outright hostility. Carroll simply views life differently than most people, and his views appear to be superior in the aggregate once they are applied to a broad range of situations.