You write:
My server has more than enough disk space, or am I completely missing the point of S3?
You are not missing the point if what you have on you server is write-once read-less-than-once stuff, such as disaster-recovery backups (which you hope will be read-never), because transfer times will not matter. The point of S3 is delivery speed.
First, S3 distributes your content geographically. End users benefit from shorter paths.
Second, S3 can act as a BitTorrent seed, which not only conserves your bandwidth, it means your most popular content will be distributed faster because it can take advantage of the ad-hoc swarm. There are reports on the AWS Discussion Forums that S3 support of the BitTorrent protocol is "very, very spotty." I have not tested it myself.
