"Proof of Personhood" is indeed a critical component of internet infrastructure. In Belgium we have an app for that called "Itsme" and it is becoming more and more the go-to single-sign-on tool. Instead of scanning your iris it asks your bank or government to confirm your identity when you set-up your account. I believe the EU commission is working towards standardising those protocols so apps like Itsme will work EU wide, maybe even worldwide.
As for privacy I don't see a big problem as for most online services I don't want to actually be anonymous towards the service provider, just towards the general web, and the online services should respect that according to the GDPR