Do you think candidates would ever agree to mic off/on in sync with the timer?

I've always wondered why, if interruptions and going "past your time" is such a big deal in debates, why the hosts don't just sync the mics to turn off and on depending on whose turn it is to speak and how much time they're given?

Or would the candidates never agree to this?

Or maybe the networks secretly love the interrupting, combative style because it makes for better drama?