IMO one good reason for striving for a very high level of sharpness is simply that it's an excellent indication that you did everything else correctly in the sharpening process: no wire edge or damaged steel remaining, entire edge even, etc. Also the blade that starts the sharpest usually will remain sharper longer.
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That's what I do, and since my knives are so thin I go for edges brought up to at least spyderco fine and usually ultra fine lately. I carefully monitor the edge formation with my trusty Radioshack lighted scope, and my edges have been sharper and longer lasting once I figured out how to get rid of those pesky burrs. Plus, since I carry at least 2 and usually 3 knives, I can always leave one with a little rougher finish for any larger amounts of cardboard or rope I run into. I have found though that for my EDC needs even a thicker (15 per side or so) edge at a very high polish holds a shaving edge just fine for several days, as I don't generally run into marathon cardboard sessions. I mainly open letters, some packages, cut some food up, all kinds of stuff. After carrying the passaround Caly 3 in SE I think I need to carry a SE knife for my cardboard and rope and other tough chores, so I can keep the rest of my knives with the nice, sharp, polished, long lasting showoff edges that I like.