Really, Facebook/Google get the sweeter end of the deal. They'll know that you use Fred's arbitrary website. They will know when you use it, how often you it, and how long you use it each time.

They'll add your new usage patterns to the database they've been building about you for the past decade. They'll correlate your behavior with other users of Fred's arbitrary website.

They already get that from Facebook like buttons on every single page

To be fair, Fred's Arbitrary Website probably only captures your email address, if that. OAuth2 permissions and the like.

But I agree, some users would rather cut out the middleman than be chained to the social network du jour.