I disagree that it necessarily makes the world run on your time.
All it does, is make the default method of communication asynchronous and forces synchronous communication to be scheduled.
It doesn't "make the world run on your time", unless you're still using a phone to interrupt other people with unscheduled synchronous communication.
The responsible way to ditch the interruptions and improve focus is to shift your own communication to asynchronous methods and expectations as well.
I leave my phone on silent (no ring. no vibe.) unless I'm expecting a particular call. I think it's vastly less rude of me to make an unscheduled caller wait until I make time to answer a message than for that caller to have presumptuously attempted to interrupt my day with an unscheduled call or "emergency" email they demand an instant response to.
I have yet to work out a good way for actual emergency notifications to ring through. But until phones provide a good solution to that[1], I'll err on the side of being more productive every single day in exchange for running the risk of being 'out of contact' in the event of an actual emergency.
[1] I've tried setting my default ringer to dead air and setting a custom ringtone for my wife. But that doesn't let me easily flip the ringer back on for when I'm expecting a scheduled call. And I'd still like an email client that will let me set a custom alert rule based on contact. I'd rather not run a second email client to watch an 'emergency' mailbox.