I presume Congress, like Parliament, cannot bind its future self, so "barring" a leader is just a pinky swear because any future Congress can just "unbar" them. The thing about beheading is that you can't undo it, cos that's not Man's law keeping them dead.

Charles I was beheaded. Even if the day after Parliament had thought better of it, their only option was to make somebody else King instead, Charles I was dead.