We want a feed without a website in order to add a podcast to an existing non-Wordpress website. I've looked at a huge number of tools, and the only one that's free, not miserably buggy, and has all the features we'd want would be Wordpress + a podcasting plugin.
You do make a good point about the feed permalinks. Hopefully either they could link directly to the MP3s, or maybe I could set up some sort of redirect.
Thanks for the suggestion!