Leadership is a useful tool in coordinating the efforts of large numbers of people, in order to efficiently gather information, develop best practices, and accurately evaluate the results of organizational efforts.
Well done, you've indeed just described the role of Whip that a person can fulfil perfectly. And you're right, you do often need those people alongside leadership. And no, the term doesn't come from literally using a whip, though I suppose it does make for some rather evocative imagery. I do really love the term "lose the whip" to mean that someone is expelled from their own party.
A whip is a useful tool to force people into coordination
It's an awful tool. It can't convey complex ideas, doesn't maintain a useful catalog of effective uses, and only works at a very limited range for a tiny number of subjects on a momentary time scale.
I might suggest replacing your whip with a library. Libraries have been far more successful at organizing and commanding large numbers of people over long periods of time. The library was arguably the most effective tool of the Pharaohs of Egypt, the Chinese Dynasts, and the Catholic Church in commanding populations by the tens of millions.
Wielding a whip makes you a nuisance. Wielding a library makes you a God.