I think you're conflating two things. Creating infinite identities is known as the sybil problem is cybersecurity, or sybil attacks. Indeed you need a way to verify identity in the real world with trusted parties to defeat this.
(In my interpretation 'uniquely identifiable' should be satisfied by your unique ability to sign data -- actions, statements, etc. associated with that key. there's a problem of making the identity itself human readable, which essentially needs a name system on top)
That said, I think the government de facto already has many useful functions around identity verification, I think making it more accessible, modern and useful is a good idea. Also with good design practices of digital systems, we can also make things more transparent, auditable, etc.. The downside I would say is the possibility of some kind of catastrophic breach or denial of service event having a large impact (any of our usual web services are subject to that though), and having a fallback offline infrastructure should be worthwhile.
Yet despite that, only one of those certs will work for my account. In fact, it's better for me - I can create a different cert for each service and I can't be tracked.
