Unfortunately many nurseries here in Texas sell Kadotas, labeled as "Banana Fig" trees. I have also seen this mis-labeling on trees from wholesale growers in south Louisiana. Which is causing much of the confusion, and is the most likely reason for the results you mentioned.
But there is supposed to be a true Banana fig. It is described as, "A medium size yellow fig with pale strawberry flesh. Very sweet, full flavor, no bitterness, closed eye, but will split if not harvested when ripe. Low spreading tree, but can also grow tall, so prune to the size you want.... Grown in Seabrook, Texas since around 1910."
This doesn't sound like a Kadota to me. Not with the pink flesh and closed eye. This is the tree that I am hoping to find.