Basebrawl, forget suspensions, sue one of them
The pitcher had hit the batter, Carlos Quentin, who has been hit plenty of times and by Greinke before, in the shoulder, prompting the charging and the brawl.
Now, Greinke did duck down and meet the larger Quentin, but I see that as responding to a very real threat. Also, there are mechanisms to deal with intentionally hitting a batter, though no one seems to be saying it was intentional, considering it was a 3-2 count in the sixth inning of a one-run game.
So how does the league handle it? It will suspend Quentin. Dodger manager Don Mattingly rightfully argues Quentin should not play until Greinke comes back. That may curb this. But how about this? The Dodgers, who pay Greinke's salary and now must find someone else to pick up wins as they hope make the playoffs, sue Quentin for something like $20 to $50 million. That might end charging the mound. They may not win... this time, but eventually a team suing may win.
They considered charging players in hockey with assaults for fights, but no one liked that, bringing in an external agencies and entity to make judgments on what should be an on-ice issue. But one team taking the other to court, bringing lawyers into it, just as lawyers end up figuring out who pays for injuries in auto accidents, well, that might get a player's attention.