Let's be honest here... I can't speak for BR, but the city of Jackson would have a mutiny on their hands if they said they were going to pick up the costs of a JSU football game. There are too many pertinent issues going on with the city right now. (ie...clean drinking water, hell just keeping adequate water pressure, garbage contract, streets, gun violence.... the list goes on). These issues all take precedence over fronting the money for football games. The "clear people" would probably get all the votes they needed from the black Jackson residents to take back over the mayor and city council positions just from the backlash of such a move...
Not saying that it would be a bad investment for the city... However, the perception and PR that would come behind such a move with the current state of affairs in Jackson...would be too much for the current administration to overcome.