writing for funsies vs. writing for cereal

So recently I read an amazing fanfiction, Personally, I'd Rather Lick Sand. And when I say fanfiction, I mean a novel length piece of ficition that is a modern day reinterpretation of Jane Austen's Pride and Prejudice but is otherwise completely original an holds its own in the literary  world in my opinion. My immediate reaction was that something this good should be published if possible. It seemed too good to molder away on a fanfiction site when it could reach so many more people if it were really pushed out there. As far as re-vamps of classic literature goes, they are seemingly at the peak of popularity, with the vlog The Lizzie Bennet Diaries sparking this off as of late into an even more irresistible frenzy. This being considered, in the book market of today, a fiction such as this one could make it in the published world if applied properly. However, is it important? Does it really have to be published or is it simply enough for it to be share with the world?

I think it is so very important for people to keep writing, no matter how they do it. Whether it be for fun or for work, based off a T.V. show, or another book, or a movie, as long as they keep doing it and keep sharing it. The publishing industry and copywriters should not own ideas and stories completely. Anyone who argues can take a look at Shakespeare and then see how far he would have gotten without more than a little inspiration. That being said, I guess it is up to the author to decide if they want to write as a career or just because they have to get it out. I really don't know if there is a right or a wrong answer to this. I know if I saw this fiction out on the shelf in a book store I would buy it and read it and love it being on my bookshelf. However, as an idea and piece of writing that is free fanfiction on the internet I still love and respect it, the same as I love AU fanfiction written for Doctor Who, Teen Wolf, or Merlin. And the same as I love the real Pride and Prejudice, or Harry Potter, or any of the other published work out there. They both give me genuine pleasure in reading them, as does anything that is done well. 

Are there any writers out there with thoughts or opinions on the matter? I'm interested. In the meantime, here is a link to the fic: totally worth reading at the way through if you like this kind of story  - http://www.fanfiction.net/s/4656343/1/Personally-I-d-Rather-Lick-Sand