A few years ago, I had a boss that completely prohibited cellphone usage (he demanded that workers leave their phones in their car) and he strictly monitored what websites we went on. Basically, you weren't allowed to look at anything entertaining for your entire shift (even on break), unless you went to the bathroom and did it there. It was so painfully boring that co-workers would look to the little headlines that popped up on the browser homepage for entertainment and a source of discussion.
I felt this was unnecessarily extreme. From my boss' perspective, I'm sure he'd say he's paying us to be there so we should be working at all times. But this perspective doesn't take into account that people's focus naturally waxes and wanes anyway. Taking little breaks can actually give you a boost when you get back to work. I've seen a lot of psychological studies that support the idea that regular breaks are a good thing.
Granted, I wouldn't want to encourage my workers to waste time, but I don't really see the need to be this strict. At my current job, the boss doesn't care if we use our phones or the internet as long as we get our work done. If it really became a problem and things weren't getting done, I would address it in some way, but not prohibit it. Maybe just say something like "cellphone use is for urgent matters only" and not bother enforcing it. And anyway, your workers can always just go the bathroom and use their phone in there. Ultimately, I definitely think that sometimes, cellphone/internet use at work isn't a big deal. It's just hard to properly define "sometimes" in official company policy. So maybe just have it in the books but don't enforce it. Or just don't prohibit it at all and simply judge the employees on whether or not they're getting their work done.