Never heard of a limit on any item as too how many times you can switch it on & off in a given period! Some cheap "hobby" rated equipment does state that it is not for continuous use (ie the motor needs a chance to cool down after a certain short period of use).
I've used several different lathes, fixed speed, variable speed electronic and variable speed mechanical and never had any problem with how often I switched any of them on & off.
It used to be thought in the early days of PCs that it was better to keep hard disks powered on than power them on and off repeatedly - which led to some offices leaving their computers on all the time (maybe only switching off the displays) - which was of course a big waste of energy and probably unnecessary as well. Some very early hard disks suffered from something called "stiction" - which happened if they were stored powered off for several months. The heads would be left on a "parking area" of the disk at power down and in storage could "stick" slightly to the disk surface and require manual assistance to get them moving again - but that was with hard disks over 30 years ago!
Some types of equipment do appear to fail more often at switch on - but that is probably because a component was on it's way out in any case, and the inrush current at power on was the final straw.