I think the main difference between the Leafs and other teams is that other teams realize the officials won't call penalties in certain moments and take full advantage.
Paul Maurice's gameplan was a masterclass of manipulating the officials. He basically told Florida to play dirty all series and then kept holding up his fingers and complaining about the lopsided penalties every post-game interview until eventually the referees end up even (or in Florida's favour) despite them running the Leafs, elbowing, and generally just committing way more penalties in a game. They were the second most penalized team in the entire NHL due to their style of play, but all of a sudden they commit no more than 2 penalties a game after Paul Maurice called them out for 2 games. That little finger trick was smart because the officials were scared of a spotlight being put on them and wanted the penalties to be similar so Paul Maurice wouldn't call them out and be shown all over the TV with his fingers up. If Keefe had any gamesmanship, he would have countered that - but he doesn't. He needs to go. He bet his job on Holl, and that ship has sailed.
The Leafs try to play the game clean and it backfires because the other team is getting an advantage with all their dirty plays. I don't blame the Leafs for trying to play clean because they seem to get borderline penalties called against them and then they just try for a clean game.
Teams like Tampa/Boston/Florida basically dare the referees to make a call in a high pressure game. They manipulate the officials. Stamkos fighting Matthews, last year Matthews being held in OT, the diving, Gudas grabbing the stuck, etc. They know the referees won't call any of those in critical moments, but the Leafs get wary to play the same way because they actually get called. Like Holl's interference in Game 7 whereas Gudas grabbing the stick is clean today.
That's why I prefer to cheer for teams that don't play dirty or take advantage of 'playoff (dirty) hockey'. Colorado was great last year, even with all the dirty plays by other 'veteran teams', they were just so much above everyone else that they would win regardless.