Eh, if I have a complete story that I can be proud of, I will definitely want it in a physical form of some sort.
As for self-publishing to a bigger market, it's a similar feeling I suppose: having something complete that you think people beyond the free websites one posts on might appreciate.
So basically the first question is: Are you happy with your story? If not, feel free to alter it until becomes something you are proud of, or at the very least enjoy looking at.
Then you ask yourself, do you want to share this with a wider audience?
As sort of a combination of the two points above: if you really want to make a story that's totally marketable, perhaps consulting with an editor with industry experience may help. They can possibly help guide you to make edits to your work so that it meets audience expectations for the story's genre.
I don't think there's ever a question if one wants to make money from something, unless it's for charity. I think everyone would like to make a bit of money from their passion.
For my own work, I'm in the process of self-publishing right now. I wanted to self-publish because it's the first full novel I ever wrote and I'm super proud of all the work I put into it, like on top of writing it I did countless rounds of edits, including a full read-through of a print proof. I really do want to share it with the world and since there is a limited audience for webnovels, expanding its reach via self-publishing is an avenue for that.