i do wonder if the world would be a better place if instead of lawyers we had cage matches

Southwest Airlines got sued by some other company over, IIRC, color schemes. Southwest's CEO (Herb Kelleher) made an offer to the other CEO: They skip the lawyers and settle it with an arm-wrestling contest. The other CEO agreed.

Eventually, they wound up selling tickets to the match, and donated the proceeds to charity.

Now that's a civilized way to conduct a lawsuit.