Mike, you raise a number of very valid points, and I think I understand your reasoning, but I am not sure I agree.
I just think that if you do that, you call attention to it, and run a greater risk of escalation than if you address it individually. From the evidence presented in this case, I have nothing to tell me that the coaches knew anything about the player's behavior during the coin toss.
"Showing everyone in the stadium that you are talking to the coaches" is fine , as far as it goes, I guess, but they don't know what you are talking about, heck, for all they know, you could be discussing what the weather or how to beat the traffic after the game. I think bringing the coaches out to midfield in a show like that, puts them in a bad light, and on the defensive right off the bat. Yes, we want to assert and maintain control, but it's better to work with the coaches, than against them.
I will always assume positive intent on the part of coaches (until I can't). Perhaps I shouldn't, but with everything that is going through their minds right before a game, I can't believe that they are thinking about the players who have been designated as leaders (for whatever reason) acting like spoiled children.
I understand only making the speech one time. In my example you would have to do it twice, but I think it is worth it to reduce the risk of escalation.
We don't know, at this point, if there were a bunch of assistants mouthing off. And if there were, I can then the head coach would also know it, so after I give the sideline warning at the end of our discussion, we will know who will be responsible the next time the flag comes out.
You don't have to have a bunch of players around when doing this, you can walk with the coach to a less crowded area and, again not make the conference so conspicuous. walking side by side, rather than face to face can also help lower the tension. Though if there are players around specifically those that acted childishly, perhaps that is a moment that the coach can assert his leadership. They are his players, he has responsibility for their actions.
Calling the coaches to the center of the field show how serious I am about what I was saying. They should know you are serious about your discussion regardless of where it occurs. I don't make a habit of sideline conversations, so when one occurs, it is already serious.
I want to talk to them on my own ground not on the coaches ground. The entire field is "my ground." But, again, I am not looking to escalate this situation, I am looking to calm it down. If I can talk to the coach where he is comfortable, I'm ok with that.
I guess your last statement is where we disagree the most. I don't think it is- or should be- a struggle for power. The rules ALREADY give me the power, I don't have to show it. I am willing to be a benevolent dictator and share some of that power with the coach with the idea that we will all be much happier that way.
I'd rather we all work toward the same goal rather than be confrontational.
Perhaps I'm being naïve. But I just think there is a different way to make this work.