"I don’t see how anyone could... do any kind of meaningful work by replying to every email in their inbox all the time so that it’s always empty"
1) You don't have to reply to everything. Triage, including deleting liberally.
2) Your Inbox is not supposed to be empty all the time. That's an impossible goal.
3) IZ is about managing your email so you can *get out of your Inbox* and do other work.