The bananas-like taste of Jack Daniels does seems a signature of the brand. The taste seems to blend well with cola. Whether the bananas came before or after the cola is hard to say (i.e., is it an intentional result to ensure an optimal mix with Coke and Pepsi or an "unconscious" evolution of the taste over 100 years and more?).
The taste is one that pleases many, but not all.
I notice it at its most intense in Gentleman Jack. Why this is so I am not sure. The second charcoal mellowing doesn't seem to remove the banana esters if that is what they are. Maybe it contributes to a rounder, smoother mouthfeel.
I like some bottlings of the Single Barrel, I mentioned some earlier in the thread, where the banana-like esters are muted and you get dark caramelized oak tones and a dark cherry-like taste. That version seems closer to bourbon.
These drinks do really change in my opinion over 30 years and more though. The JD from the 70's I tasted with Mike Veach seemed different than the current regular JD, not just because of proof. I have some 70's Dickel which does not show the "vitamins" flavor some have noticed (including me) in the current bottlings.
I think the JD "taste" where it is most accentuated probably results form a combination of the particular yeast used and perhaps a high fermentation temperature.
I believe all the bourbon makers (I include JD in this in a broad sense) ferment at an ambient temperature but e.g., are the fermentation rooms cooled in the summer and heated in the winter? I don't know, this is something not often discussed here.