Identity Theft is a completely made up thing, that used to be called fraud. When it was called fraud it was the responsibility of the institutions to protect themselves. Instead they use the word identity theft to make it the problem of the victim. If someone goes to the bank and pretends to be me and gets a line of credit, spends a ton of money, I am left holding the bag since it destroys my credit rating. Yet, I didn't do anything at all wrong. These institutions rely on woefully inadequate measures to determine identity and when something goes wrong, the person who should pay for inadequately verifying identity is the financial institution that messed up and gave credit to the wrong person under false pretenses.
Anthem is my insurer and now I'm responsible for dealing with the fallout from every institution's completely inadequate processes for verifying identity. How is that fair?
The solution isn't hard, you'd get an account with an identity signing service that goes to great lengths to confirm your identity. Once your identity has been confirmed, you either generate your own private and public keys and upload your public key to them or they can generate both on your behalf. After that, you either host your own service to sign with your private key or you redirect signing to the identity provider if they generated a key for you.
This is not a pipe dream. It just requires mandating that companies need to require that you sign off on things cryptographically. If you have not signed off, then the losses and consequences from fraud are their responsibility, not yours.