Yes, this isn't implemented as something you can integrate with over the internet using SAML 2.0 or oauth or whatever, but it still happens with much older tech (writing + paper + anti-counterfeiting tricks + bureaucracy).
James C. Scott's book "Seeing Like a State" makes a pretty good argument that the state wants to arrange society in such a way that it is legible and tractable to central bureaucracy in such a way that the state can efficiently pursue the state's goals -- collecting taxes or crushing political dissent or so on.
So separately from if the state "should" do it, or if it is a "good idea" or not, the state will do it if they think it will help the state achieve its aims, and the population or some other powerful party doesn't resist it.
When does something officially become recognised infrastructure?
Streets, power supply, water, and now we are actually facing the question if the internet should be part of the default infrastructure we expect.
This poses several questions and issues, such as identity but also e.g. storage of data. Think of all the SaaS products, and what happens if they go out of business.
What happens to your data? In a more broader view this means, who owns the data? You, the provider, the state, nobody?
But Estonia, through e-Residency and other initiatives, is largely trying exactly that. They've met with some failures and some successes. Human beings are still pretty new at this "government" thing.
Please Google/wiki self-sovereign-Identity.