I agree that (not unlike many aspects of Shopify functionality), the way their archive feature functions is useless. I did finally find a relatively easy workaround for this particular issue though, so I wanted to share.
Archived items seem to no longer be active on any sales channel, so you can use the ‘Availability’ filter in the inventory view and set it to whichever channel has all of your products on it (for me it’s my POS, since I don’t carry everything online that I do in-store, but I do carry all items I have in inventory in-store). This filtered out all of the archived items for me.
Hope that helps! Wish we didn’t all have to constantly come up with dumb workarounds to things that should be built-in functionality to Shopify.