They are trying to use a technical solution to address a social problem. Train the people to be professional and respectful of their co-workers' time and the problem will take care of itself. Besides, if my incoming emails become too troublesome, I adjust my notifications, and deal with the emails when I need to, not when they arrive. I don't want the company controlling that valve for me. It's a clumsy way to try to address the problem.
Insufficient escape velocity. I keep getting drawn back in, so valuable time and attention can be extracted from me.
Take care of the luxuries and the necessities will take care of themselves. -- Lazarus Long