Does anyone know of a company that offers a hosted-type service where a public user can create an account, pay a fee, and create / share a sharepoint-based website with others?
I do not know of any currently existing websites that offer this, but you'd be looking at setting up a website (outside of SharePoint) which would be where users pay you the (recurring?) fee for access to your site. As a user, they would have access to your community and be able to share their sites with other users, although they would need to create their site through SharePoint, not your site.
Something you may want to consider is running ads instead of charging users to become members of your site. This would help decrease the barrier to entry and make the initial growth of your site a smoother process.
If you go through with this, I'd be interested in what your site has to offer! Best of Luck!