The SEC forced that trophy on LSU/Arkansas. Neither LSU nor Arkansas fans really care about it. The only thing they care about is who wins the game when it has SEC West implications. Arkansas is the new kid on the block in the SEC and LSU doesn't have a "real" rival.
That the two schools from neighboring states become rivals certainly makes logistical sense, but you can't force the kind of hatred on people that it takes to create a rival.