Fat chance. These teams seriously dislike each other. There were players on both sides who deserved a decent slap from Broad.
Then again, this is a match referee who, during his playing career, once refused to leave the pitch after being given out lbw in Pakistan in 1987-88 and had to finally be persuaded by his opening partner to trudge off; and also smashed his stumps over with his bat after being bowled in Sydney. Just the man to be responsible for keeping order on the field.
It needs to be said that the final day of this test was totally captivating, gripping television as India charged to victory. But the level of much of the behaviour, led by India's highly flammable captain Virat Kohli, did the game a disservice.
Kohli, Mitchell Starc - gobbing obscenities at a departing batsman - and Australia's skipper Steve Smith deserved punishment, as a minimum.
Smith's looking up for advice from the Australian viewing area on his lbw was bang out of order the batsman. Smith claims he had a brain fade. Maybe, but that's not an excuse.
The animus between the captains through the match was deeply unpleasant. They are the men charged with upholding their players' standards, or at least that used to be the tenet. Kohli certainly led from the front in at least one department.
He later accused Australia of being serial cheaters, although he wouldn't say the actual C word. But his relentless sledging and encouragement of unsavoury behaviour of his players means he should have had the spirit of cricket book bounced between his eyes.
There's a view that the ICC are reluctant to take on the Indian skipper, given his standing within the game in his country. Having just regained authority from cricket's self-anointed Big Three, India, England and Australia, they don't want another punchup with the Indian board.
Kohli is a man who pushes the limits with his behaviour.
The boards of both teams understandably went in to bat for their captains. Get this laughable statement from the Indian board: "Mr Virat Kohli is a mature and seasoned cricketer and his conduct on the field has been exemplary".
Returning serve, Crickat Australia's chief executive James Sutherland offered: "I find the allegations questioning the integrity of Steve Smith, the Australian team, and the dressing room, outrageous."
To which Richardson offered a limp: "We have just witnessed a magnificent game ... where players from both teams gave their all and emotions were running high during and after the match."
Former West Indian skipper Richie Richardson has replaced Broad at match referee for the last two tests. He will deliver both captain a talk "reminding them of their responsibilities to the game". I kid you not.
That's okay then.
What the ICC's non-action also means is a door is opened for players in other test matches. They can point to the farce in Bangalore and tell a match referee, if called to answer a charge: 'you let that shower go unpunished in India, so you can hardly ping me." Watch out for double judicial standards in the wake of this match.