That sounds like a terrible idea to me, I'd never want to do that. If they like the work I do, management should learn to respect the way I do it.

Sometimes there are genuine emergencies. If your company got hacked and is all hands on deck, you kinda have to be interrupted. There are situations in which emergencies may not be paged through normal systems.

If you have the kind of clueless/toxic manager who is going to abuse this sort of arrangement, they are probably never going to agree to this sort of arrangement in this first place.

For nearly all working relationships, I think it's reasonable to keep an emergency communication channel open.

If you like the company/team enough to work there, you should learn to respect the way it operates.

Hopefully it doesn't sound too combative, but I wanted to express that it's a two way street and compromises have to be found. I dislike various things in my company on a personal level, but often make sense from company/team point of view.