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.