Because if it doesn't hit my inbox I'll never see it at all. The archive is great for looking up stuff ("What did I pay for Slicehost last month? Did Mary Smith get a purchase confirmation?"), but not great for push notifications. Non-priority emails in the inbox are, for me, a good compromise in terms of amount of distraction caused per unit of actionable info gained.
I have a bunch of filters setup to archive but also label them as "Skim". So I see in my sidebar when there Skim has unread messages, and I get around to reading them when I have time.
I could just have those filters "Never mark it as important", but those messages are less important than stuff in the not-important part of my inbox. It's stuff like high-volume mailing lists that are never urgent. I'll let Skim go for 2 or 3 days if I'm busy, whereas I like reading all email in my inbox within a couple hours of seeing it.
