I check email when I arrive in the morning, before and after launch, and before leaving the workplace. Those are the moments I am "off the zone" anyway. It's a good balance for me and I never miss anything important.

Indeed. I will add to that, when I do allocate email time I answer carefully, don't fob people off and make sure everyone does get an answer. That is better customer service than a person who gives snap replies just to be fast

That just doesn't realistically work for most professions that rely on email. Your email just sounds like something personal that doesn't require any reasonable attention.

It works fine if it's the expectation that you set.

Sure, customers will just find someone more responsive.

If you're attending customer requests, that's productive work, right? That's not what's being discussed here IMO.