This is certainly not an informed opinion about the specifics of Atlanta, but generally in a place like that the core city should stop trying to cajole uncooperative suburbs into forking over money to improve regional links, and instead try to improve the "getting around the core city" aspect of transit.
Too often mass transit in the US is seen as a way to solve the problem of highway congestion. It isn't actually a great solution to that especially if people affected just aren't interested.
In my urban hellhole, 2 out of 15 transit authority board members are from the city of Philadelphia and the rest are from the burbs. It's not even close to being representative of ridership.
