Old E-Soul has been around for forever right. And every glimpses we see of him from any point in time, he's missing his arm.
E-Soul taking out Zero is implied to be (near) the start of the commission's timeline. He's implied to have become X after that. In the opening when they're showing us all the previous X'es he's missing an arm.
Maybe a missing arm is as intrinsically tied to E-Soul as his electric powers. So much so that when Yang Chen took over as E-Soul, the people's subconscious certainty that E-Soul's missing an arm fucked him over and that's why Yang Chen lost his arm in that fight.
Like would that be fucked up or what