I have actually been on the other side of the hiring process. The best candidate that ever crossed my path was a Microsoft employee who was a high school dropout and applied anyways for a position asking for post-secondary qualifications (e.g., community college or university).

I've never been drowned in resumés so maybe my opinion would be more along the lines of yours if I had been. It's a job seeker's market up here in Toronto. I think the most resumés I've had to deal with for a particular position is a couple of dozen. When I was hiring I would only post the job ads at places like JoelOnSoftware's job board. I'd never post it on Monster as I consider places like that to attract too many poor quality candidates.