But you can star something without moving it out of your inbox. It then moves up into a separate list at the top; the delineation is very clear, and I don't have to bounce between different screens.
Things you don't want to see again should absolutely be archived. But if you're using the Gmail web interface, you don't have to slavishly adhere to a literal interpretation of "inbox zero".
It's not about the label "inbox zero". In fact, I rarely have an empty inbox. Usually there's a handful of unread messages and maybe a couple that are read, but I haven't decided whether they need action.
What is important is limiting the distraction caused by new mail. If you're working through your todo items and new messages are getting added to the list, they'll distract you even if you don't read them. Of course, you probably will read them, which is even more of a distraction.
By keeping todo items on a separate list, you can keep your attention on your work, rather than on new messages. Then you process the inbox only when you choose to direct your attention to it.
Things you don't want to see again should absolutely be archived. But if you're using the Gmail web interface, you don't have to slavishly adhere to a literal interpretation of "inbox zero".