No - if it's mutually, it must obviously be "ourselves" if the subject is "we". Note that the English sentence is fine without an explicit "ourselves" - the "each other" in combination with the subject "we" unambiguously identifies the object as well.
Esperanto needs the "nin", yes, but you can't say that it does so because of some logical necessity.
It is not because a speaker of languages where the object wouldn't be needed doesn't understand the sentence. It is needed because "helpi" is a transitive verb and requires an object.
English also is totally fine with saying "The door closed".
Native speakers of eg. Esperanto or any Scandinavian language would sit there waiting for the rest of the sentence: The door closed... what? The door closed the locker, the car, the book?
So to speakers of other languages "nin" might be a logical necessity here.
I don't know that that is true. How about "We helped them reciprocally"? Of course, with "each other" it is implicit, but Esperanto doesn't have "each other"; what it has is more closely equivalent to "reciprocally". Even in English, when you use that, you still need the object.
ourselves is reflexive while each other is reciprocal.
If you have Peter, Paul, and Mary, and they all help themselves, then Peter helps Peter, Paul helps Paul, and Mary helps Mary.
But if Peter, Paul, and Mary all help each other, then Peter helps Paul, Paul helps Mary, and Mary helps Peter (for example).