Do what works for you. I absolutely love email. I'll pick up the phone and call someone too, but most things I do aren't so urgent I need to call you and interrupt whatever you're doing right this second so that you can give me your full, undivided attention.

I use email to remind myself of things I need to follow up on, coordinate events, and keep new engagements in a single stream of consciousness. It works well for me.

I don't typically get to 0-inbox, I usually have maybe 10-30 emails in my inbox which are all read and are all there for a reason (listed above and more). I religiously unsubscribe from things (or don't subscribe in the first place) and I will admit it takes some work to keep organized.

I also have all notifications turned off and my email only fetches once/hour anyway. I actually get excited when I get new emails because typically there's something in progress and it's some sort of update or new information I can use to do something I want to do.

So there's nothing wrong with a no-email policy. But I there's also nothing wrong with email. Everything comes down to the processes YOU like and find the most beneficial.