I found this interesting.
As a Mediterranean species, Ficus Carica much prefers California to anywhere on the East coast. But, of course, there is a wide band of territory in the east where figs can be grown rather easily and nearly maintenance-free. Basically, east coast 7b through 9a. From coastal south Jersey down through coastal northern Florida (St. Augustine, in particular), the only trick to growing them seems to be to stick them in a hole in the ground, water them liberally the first year or two, then harvest the fruit.
So, when you described them being a problem in your location, I could come up with a couple of possibilities. One, it may be just too warm in your winters. Maybe figs want a little chilling time in winter. They would get that through 9a. More south of that? Probably not. Two, your year round heat and humidity might stress the species out. Again, northern Florida's "winters" might provide just enough of a break to keep the trees and fruit a good bet there.