Splumonkeys will pick Bananas from Cave Banana Trees on sight, which has no effect on the 4-day regrowth period of Bananas. Splumonkeys also are more likely to follow and steal from a player if the player is carrying any number of Bananas. Bananas are also eaten by Prime Apes in the Shipwrecked DLC and can be fed to them to befriend them.
The raw image for the Banana shows multiple bananas in one bunch, but the Cooked image shows only three, which seem to be poorly prepared. This could hint to poor cooking/preparation due to abnormal food.
Wickerbottom's quote mentions that all of the bananas are genetically identical. This is probably a reference to the concern from botanists over the increase in cloned banana trees which could theoretically make them infertile. This could also be the reason Cave Banana Trees cannot be grown by the player.
The Cave Banana name is possibly a play on one of the most common banana cultivars, Cavendish Bananas.