Wow, that idea would be sooo coool. Take out all the boring stuff of normal problem solving (all that boooring talking and yapping they constantly do at those lame court shows) and replace it with something super awesome (people fighting).
But seriously... weren't you taught to solve your problems in a civilized manner, by talking about it? This show would have all the degenerative properties needed to fulfill Idiocracy's vision of the future. Wouldn't this show encourage people do get violent over solving problems?