I think it's fairly clear that despite the workarounds proposed, the use case for Archived notes is rock-solid. Don't workarounds generally suck, and annoy the user each time he/she uses one?
The primary benefit of the feature (for this user anyway) would be a less cluttered default view, but faster search (assuming default search would exclude Archived notes) would be a collateral benefit. Another (obvious) use case: if one used Evernote to satisfy IRS requirements for document retention, you simply want such stuff stored securely, but you don't want or need to see it...hopefully ever!
Would some users prefer a more benign name for the requested feature/functionality, e.g. "Hidden" notes?
I'm not a software developer, but implementation of the feature would seem dead simple: a button could be added to the New Note window (e.g. next to the Reminder button) to select the Archive/Hide feature--it would be OFF by default. In turn the main view would exclude Archived/Hidden notes be default.
What could be simpler? (...asked the ignorant user...)
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