This idea is sort of the opposite of what is happening at the moment where Facebook and Google authorise people to use other websites. Sign up everywhere is a service you join where you control your information and can use the service to sign up everywhere else.
A benefit of the service could be that Google and Facebook would no longer know where you are signing in so it might cut down on tracking. Also the website itself might no longer know who is signing in. Only that they are authorised to do so.
Although there are lots of providers of OAuth, there don't seem to be any that are purely authentication providers, just large companies that offer the service.