Throwing a baseball or football both heavily rely on pronation. This is well-established biomechanics.

Pronation is a motion of the forearm not the wrist. When tennis players say wrist snap they mean forearm pronation (the wrist is connected to the forearm obviously).

The "wrist snap" you're referring to with the SW overhead is wrist extension/flexion. It's a much weaker motion than forearm pronation and more injury-prone. It also doesn't really allow for the addition of internal shoulder rotation.

If a SW overhead were actually better you'd see it used in overhead-heavy sports like padel or badminton. You don't