The GA runoffs proved that he has little suburban crossover
That is actually not true. Perdue outran Trump by 6-10 points (maybe even more in some precincts) in much of East Cobb, North Fulton, and Buckhead. Some parts of Fayette, DeKalb, Oconee, and Chatham did too. In other words, there's some crossover among white suburban voters. The problems were that rural Trumpy/Stop the Steal turnout (especially in MTG's district) just tanked and that Perdue did not have much crossover in diverse suburbs like Gwinnett (which got bluer)
Apart from Cobb and Fulton and a few other counties in North Atlanta, Ossoff outperformed Biden in North Atlanta. South and East Atlanta swung D.