> For example, consider the stackexchange family of sites. They are clearly related, have a unified branding, etc. but are on separate domains. On Firefox, which blocks third party cookies, I have to log in to each of those domains separately. I can't log in to stackoverflow.com, then go to superuser.com and already be logged in. That is a problem that First party sets would solve.

Other sites seem to handle this fine with redirects and cross-origin headers. Sure, at some point you land on "signin.foo.com", but from the user experience you were authenticated without having to sign in again.