I tried that but found that this worked much better for me personally. Also I had emails in very different levels of "response required" - email lists (don't need to look at vs response required immediately).
Also a big plus of this approach is feeling like you are "done" with email. I know it seems a bit complicated but its actually quite simple - most of the setup is a one time upfront cost of about 20 min. Try it out and let me know what you think about this strategy!