After Louisiana voters vote for independence, states from the rest of the middle of the US would follow Louisiana out, to avoid being dominated by California and New York, so we’d be guaranteed some teams to play with.
As our state government negotiates the details of independence with Congress, sports teams could negotiate. Because of the money involved, it’s likely that there would be little change to leagues. MLB, NHL, and NCAA all already include foreign teams (in Canada). The NFL has discussed expanding overseas as well.
