That's not really true. If the drive is closely rated to the motor size, then the drive will trip on over-current if you close the contactor when the drive is on. If the drive is oversized, then closing the contactor while the drive is on won't hurt a thing. Neither the motor or drive would care, but in a single motor application like this it does not make sense to do this.

For example, my surface grinder spindle is a 1 hp motor. The coolant pump is 1/6 hp. I run both off of a single 1 hp drive (I don't exceed the drive rated amps). I slam the coolant pump on/off at will with a contactor when the drive is running the spindle. Works absolutely fine.

The trick is the drive must be able to provide the inrush current and the drive needs to be set up in volts/hertz mode. For a mill you prefer sensorless vector mode because you don't lose torque at low speeds like you do in volts/hertz mode. No issues if you don't run in volts/hertz mode at low speeds.

My mill is volts/hertz (so old it don't have sensorless vector mode) and I can stall the motor at very low speeds.