E-mail becomes a lot more manageable if you create a filter for every kind of automated message/mass-mailing you get. At least if you're not in a position where everyone and their mother needs something from you.
Inbox zero is not at all about answering every email in your inbox, it’s just about reading and deciding if you need to do something with the email. If yes, then you move it to another folder. If no, then archive or delete. It’s very helpful for productivity, so exactly the opposite of your point. You can choose to ignore the actionable ones, or only process your inbox at certain tones, etc...
I should've put "answering emails or inbox zero." Nobody answers all their emails, right? Well, maybe some people do...
If I don't do anything with an email, I just leave it in my inbox. Currently, I have over 17,000 emails in my personal, and over 8000 in my business inbox.