It's not only in the South. In major market radio you are told, lose the heavy accent or lose the job. Regional sport-casters, when it comes to accents are a whole different ball game.
The radio & even TV sports related CEO's overlook the accents since it draws in the local listeners, thus they will hear the local commercials, and that's what sells in a sports 'local' & also 'rural' sports markets, and to a degree 'very local' talk show markets in mostly rural listening zones.
How does one lose and accent?
That's too bad, I guess. So when did NYers decide that they didn't want any more Mel Allens or Red Barbers? Or is this just a personal preference of yours?