I don't actually like governments owning the identity layer, but then again I am of the "necessary evil" school of thought regarding most of what governments do. It's marginally better than having corporate monopolies own it.
I'm a giant fan of decentralized identity, but there are two insanely hard problems with it:
(1) People lose keys, forget passwords, or get them stolen. They also lose or break security key hardware. I've heard stories of people paying people to actually excavate dumps to find lost Bitcoin keys for example.
(2) There's a chicken or egg problem of getting sites to support any decentralized login scheme without a monopolist like Google pushing it, and the latter have no reason to do so since they want to monopolize the identity layer.
Problem (1) is solvable to some extent by having companies that escrow keys for you. Escrowing with them would not be mandatory but they'd offer a "break glass" service for people who are willing to trade a bit of (potential) privacy for it. A good escrowing service would have a terms of service that forbids misuse of your identity.
Problem (2) is probably harder. Big tech will actively refuse to support any system that doesn't hand them a monopoly or at least an oligopoly.
BTW this is one area where cryptocurrency could have found an actual bona fide beneficial use case! But it's not as profitable as running scams and casinos so nobody did it.
This is a good thing because this is what people have, one single immutable identity.
What you've identified are problems with assumptions about the relationship between various things and identity.
A key one is the relationship between name and identity. Two people can have the same name but aren't the same person. A person ca change their name but they haven't become a new person.
I can do anything I want to myself honestly. I can color my hair, have a sex change, lose weight, gain weight, have height augmentation surgery, get piercings grow a beard, change my name, whatever, but I'm still the same person. That is immutable. I still have the same mother and father, the same birthdate, lived in the same places, attended the same schools, studied the same things, etc.
My identity as far as the government is concerned is still tied to a single number. Yeah, they make it hard to change a lot of the other stuff related to that number (for good reason), but ultimately they are pretty good at knowing who I am based on that number.
They restrict people to a single immutable identity, that may not conform to other governments, that may not accommodate different languages and character sets, that are not flexible of gender, that do not reflect relationship types that aren't typically monogamous... the list goes on.
They offer a poor base implementation that is only sufficient due to the legal identity seldom actually being needed online. Which is a good thing, because identity theft would be so much worse if that was everywhere.
In the UK we don't have as fixed an idea of an identity as people think, Cherie Blair is also Cherie Booth Q.C. , Elton John is also Reginald Dwight, and for both people, both identities are real identities and sufficient to get bank accounts in the name of, it's only when it comes to a tax record and passport that you are reduced to a single identifier, but who is to say that the name on that is the preferred name of a person?
My bank account, bank card, accounts on most of my things, do not match my passport and birth certificate.