You're right, its not a great analogy to think about it in terms of current flows, but on the flip side, it totally is about the flow of electrons. When you get right down to the bottom of it, nearly everything boils down to that electron transport chain.
Sure, chemistry is ultimately just quantum mechanics. Oxidation was always explained as an electron exchange in chemistry. It's just not electron flow.
Yes, except in biological systems you can chart out long chains of consecutive electron exchanges such that you end up with electrons transferring between two molecules with the intermediate molecules remaining the same in the end.
In my mind, this makes an analogy to electrical systems, for example a simple battery powered circuit more acceptable.
Still agree that connecting it with 'current' is probably not the best approach.
