We have something vaguely similar with "BankID" in Norway. It's a bank issued digital ID that submits a 2FA to your phone (not through SMS, but through some other system that takes over the whole screen - not sure what it is).
It's usable for almost all government agencies or official stuff online here, but I haven't seen anyone use it for third party auth as it costs roughly 10 cents per login for the service using it.
This has been rolled out and in use in British Columbia, Canada as well. We have a digital ID app for iOS and Android, which you verify your ID with first, then for government sites (e.g., health records), you login through this app instead - there are no emails, usernames, or passwords involved.
From a usability standpoint it's not very good though. The experience differs from phone to phone and it kinda feels like a hack from a programmers point of view.
In Norway, Sparebank1 is pushing an app to get one-time codes now. I wonder if we'll see more of these in the future?
I use the Microsoft authenticator to get access to my Microsoft work account.
I bet if everyone starts making their own apps for one-time codes EU will demand a single app to do all of this.
It's usable for almost all government agencies or official stuff online here, but I haven't seen anyone use it for third party auth as it costs roughly 10 cents per login for the service using it.