Even in the land of the free, fighting in public is illegal. It is disorderly conduct that disturbs the peace. And keeping the peace is part of the social contract.
You didn't sign that contract but were born into it, and being a member of society means following certain rules of behavior that keep a general sense of peace. Ignoring those rules by brawling in public is a criminal offense, punishable by fines, jail time, or both.