It would be a viable alternative to the ad supported model.
Most websites operate on very small fractions of a cent per pageview, you would have to have an extremely low overhead to make it work.
Say you pay a monthly subscription to the payment service provider, they then do all the bookkeeping based on a .js tag that is embedded on the page that you visit.
If you don't have an account the .js redirects you to the signup page for the payments service provider, you register, pay your initial fee and continue to browse.
You might even end up saving online newspapers in the process.