It's a delicate balance. When I was in a manager-of-managers position, I didn't explicitly micromanage how managers ran their teams or run their days. People don't respond well to that. Instead, I tried to lead by example by setting my own focus hours, giving ample notice for upcoming meetings, setting expectations for response times at the tops of e-mail messages, and so on. If you try to create an atmosphere that fosters sustained focus throughout the whole company, people tend to notice. If a specific manager becomes bad about interruptions, we'd have an offline conversation.
> I'm not sure if the distractions you're referring to are people just scrolling through twitter all day and not working or actual work distractions.
It's not an either-or. It's always both. It's not uncommon for juniors devs to complain that their workplace doesn't let them focus while their phone buzzes every 5 minutes from some notifications that they've opted-in to receive.
Work distractions tend to trigger people to check Twitter, HN, Reddit, or other sites before they get back to work. It's easy to turn a 5-minute work interruption into a 15-minute break because getting back into focus is an uphill battle. It's much easier and more enjoyable to catch up on those notifications on your phone.
The difference is that people tend to overlook the distraction of notifications they like, and instead blame everything on the notifications for distractions they don't like.
One of the most valuable skills people can learn is how to return to focus quickly. That's not to say that distractions are okay, but it's up to the person to cultivate a habit of descending back into their work as efficiently as possible when interrupted.