A polarity reversing switch will instantly change the direction of the
motor, regardless of whether it is in motion or not.

Well.... sort of. That is only true when reversing a DC motor or a three-phase
motor. Reversing a single-phase motor will do nothing since the 'reversing' is
done on the starter circuitry to get it initially spinning in the direction you
want.

This is
incredibly dangerous.

Somewhat true for motors that can reverse while turning. The danger is if your
stock is mounted with a screwed on faceplate or chuck. The sudden, opposite
torque can unscrew it. Of course, it may also tighten it even further depending
on the threading and rotation direction.

If a lathe can handle starting torque then it can handle the same torque that is
applied when reversing.

Dan