Your anecdote about the differences between coaching and teaching is insightful and illuminating.
I also agree that public criticism of players is common and arguably viewed as acceptable, while arguably not permitted by a non-coach teacher. (Could Professor Charles Kingsfield survie in academia today?)
But I see a distinction between public statements, which might not be laudatory, and true humiliation.
I think we can all agree that (in public) calling someone a useless POS is over the line, while asking how on earth a basketball player could blow that lay-up is not over the line.
So the question is - how do we draw the line?
My worry is that in today's "get a trophy for showing up" environment, the line gets drawn in the wrong place.
I grant that any coach who stated that "I'll tell them once, and if they ever screw up, they're out of here" is not going to be a coach for long. But if a coach tells me that they will explain what is necesary again and again and again, but there's a limit—I don't see a problem. And while I get that it would be uncomfortable for a player to identified as failing that rule, I don't agree that mere discomfort rises to the level of "humiliation".
I'll also note it isn't my style to act that way, but I have no illusions that I have what it takes to be a top-ranked coach. Yes, it was uncomfortable to hear, but I don't agree it qualified as humiliation.