Here in Norway (and probably Sweden, too) BankID is a widely used authentication system, and most domestic services will use that as a auth / login. Only "drawback" is that it requires 2FA, which is quite trivial today. But there are still tons of users that want their "login with FB / Google / etc.".

And a last but: If using such auth systems, one would have to account for all the different systems unique to countries.

Maybe some larger EU-specific ID / auth system would make sense?