You bring up a great point, though likely not the one you were trying to.
You mentioned Florida basketball as being a team in that group that has deeper history, better facilities, and better name recognition. Florida basketball has exactly 20 years of any of that. Prior to 2000, Florida's basketball resume looked eerily similar to Georgia's. A football school with 1 Final Four, and a couple S16s in their history. A program that was generally neglected because football is king in the south. They hired a young, unproven coach from Marshall University in 1996 with a career record of 35-20.
The rest, as they say, is Florida basketball's history. With Billy Donovan's success came a greater fan following, which brought more financial support, which brought more success on the court, which brought more name recognition, and more success, and eventually the perfect recipe for back to back national titles. If you had told a Florida basketball fan in 1996 (assuming you could find one) what would happen 10 years later, they'd have laughed you out of the building.
Why can't that be Georgia if everything falls their way? What if Billy Donovan had gone to UGA in 1996? What inherent advantage did Florida have over Georgia? Not location, not recruiting base, not tradition, not name recognition, not support.