<<..have wheels...instead

Aren't the "[steering] wheels" in all aircraft called "sticks" no matter their ergonomic(?) design?

Even if they weren't, the inference you make would likely be flawed by anachronism since the expression probably still predates the modernized cockpit.

In any event, the notion of witches hopping on their broom sticks is certainly just as suggestive as the term "joy stick." ;)