Good for you, Ally! I'm glad you asked.

I still don't know, but I am wondering then whether it is just because we are so habituated to the phrase "turn on" and "turn off," and that "cut" is not viewed as a termination of something, but just another verb serving the function of indicating some action with a preposition, as "turn" might be. Or maybe there is the sense of "cut" as a "shift."

Not an explanation, but an attempt. Have a great spring break!