Points
What do you have: 2 TX, 2 LA, 1 AR, 3 MS, 2 AL?
True, the SWAC "center of gravity" is probably somewhere in Louisiana, and historically the SWAC was pretty much TX/LA/MS/AR, but perhaps someone in the SWAC hierarchy was thinking down the road about SWAC expansion into Atlanta, Florida or perhaps South Carolina.
As far as tourism, I think what Birmingham offers is vastly different and decidedly more family-oriented than N.O. but that's only a factor for the one game a year, the SWAC Championship Game. The other 365 days the SWAC is conducting the business of the league just like any other business/corp.
Also, today it's all a game. Any entity like the SWAC, the SEC, the MEAC know that they have accumulated financial impact that they can sell to a host city in exchange for incentives, concessions, etc to relocate.
Maybe New Orleans kind of rested on its lorals thinking the SWAC would never dare leave N.O., Birmingham/state of Alabama officials snuck in with an "incentives package" to relocate and N.O. got caught nappin. It happens to Birmingham all the time. As soon as the SWAC's contract is up in Birmingham, they could be in Nashville or Little Rock,,, just depends on who has the sweatest incentives package.