I don't see how that would work as in many jurisdictions, email is an accepted legal way to communicate between a company and a customer. So when you don't year your email that's like not reading your snail mail in the 90s. It might go well for some time, until you miss that one message about a late payment or something...
Ignoring email works just fine, as evidenced by the fact that the majority of people I know don't check email unless it is for their work. Zero impact on their lives. It is the same with snail mail. I think I check my snail mail 6-8 times per year mostly so that the letter box doesn't physically overflow with junk.