I get the concern about playing on a field without a good organization to keep it up, but I'm a fan of playing in Jackson and the Coast. I'd also be good with playing at Autozone in Memphis if it's still good. Tupelo is a little too close to Starkville to justify.
You get a neutral field game for RPI and give your fans a chance to see a midweek game when they aren't close to Starkville. Seems like a win/win. Not sure if it's still this way, but I believe we used to get screwed when we played Memphis in autozone park and it was treated like a neutral game instead of a road game for RPI purposes. If it weren't for that, I'd say play a Memphis midweek game every year.
Similar to why I'm not too upset when we play road games in New Orleans, Mobile, Hattiesburg, Memphis, and Birmingham. Football is a little different because it's not as hard to get to as a midweek baseball game, but if you have to play on the road against G5 teams for financial reasons, might as well do it in places close enough to give fans an easy place to watch.