5 minutes is plenty of time to grab a flag and try to plant it midfield.
Once a fight breaks out, I'm not sure what the coaches can do? And what is the penalty going to be, fines and suspensions of the coaches?
And TV wants to interview coaches and players post game. While they can do it in the locker room, it's faster and easier on the field. Truth is, TV probably likes showing the fights, too.
I'm not sure how you teach respect and sportsmanship to young adults raised differently. It's hard to tell someone "it's just a game" when they are paid 6 or 7 figures to play that game. But there is mo need to disrespect your opponent; leave that to the fans.