You're not missing anything: the audio player on the Reader doesn't have a stop, just a pause. It does not seem to use power when it's paused, however, so no harm done, I suppose.
What you have to watch out for is leaving it
playing without realizing it -- that'll drain the battery flat in about 10 hours.
I removed all audio files from mine, and use an MP3 player to listen to them -- better sound, better battery life and it's not so big that it's any sort of burden to carry around.
