If the main argument is saving the motor /switch vs. saving your vinyl?
Neither, the argument for leaving the motor on is that the vast majority of motors take a long time to fully speed stabilize and hence you are best of to avoid turning them off if you can avoid it. Provided your mat is not "sticky" then there’s no real risk to the disc in taking it off a moving surface. In the case of my deck where the platter is coupled via magnets to the motor I can stop the platter while leaving the motor running so I tend to leave it on