Clearly, but what I propose is not that the eel doesn't work. It is obvious that it does. I think there is a different explanation for it than just that the electric field surrounding the eel in a usual dipole shape is powerful enough to force a current through another fish.
Furthermore, your wording seems to indicate that when people talk about "firing" the organ, they mean that before this, it was at electric equilibrium, and then it "fires" by the eel separating the charges in just a few seconds. That would require the eel to produce a gigantic amount of energy in a very short period of time. I was under the impression that it gradually built up the separation over time, if this is indeed the case and the electric field surrounding it can produce a force strong enough to drive a current through a remote target, then it would constantly be electrocuting everything around it, which I don't think is the case.
So, if it is the case, as you suggest, that the eel electrocutes things just by becoming a dipole and the electric field around it is strong enough to force a current through other fish, then one of the following must be true:
1 - There is no "firing" of the organ (The fact that I have seen reference made to this "firing" or "discharge" in a number of places makes this seem unlikely) and the eel produces an extremely high potential difference within itself.
or
2 - Usually, the eel is at electric equilibrium, it only separates charges when it is attacking. This would require the eel to produce a huge amount of energy very quickly, and it would be incorrect to call this a "discharge," because it is going from an uncharged state to a charged state.