I've seen this done a lot recently--including authors who are selling short stories or collections thereof as ebooks, particularly in between releases of novels in a series--and I think it's a fabulous idea.  As you said, it has many writing benefits for the author; I myself have written a few "just for fun" short stories with the characters from my 
Peter's Angel saga, and it was a great way to experiment with their characters and get back into their "voices" after a break.  I released them for free on my blog and HW, and they were well-received.
As you said, these short stories (I've also seen a novella or two with the same idea) can be great for use as free content on your site.  I'm also seeing a huge potential market for selling such work, if you've already established an audience.  Just yesterday I read "Free Four," a "short story" Veronica Roth, the author of Divergent, released as an ebook in between books 1 & 2 of her trilogy.  She took a scene from book 1 and rewrote it from another character's POV.  For people who enjoyed the book, it was delightful, and I had no qualms about paying a buck for it, even given how short it was.
http://www.goodreads.com/book/show/13615258-free-fourSimilarly, Jordan Smith released a short story collection featuring characters from his as-of-yet unproduced screenplay.  A bit of a different concept, but still very nifty:  
http://www.goodreads.com/book/show/1734 ... er-storiesIn other words, I agree--great concept!  Go for it.  I hope to do it myself one day.  
