The hard part of this isn't that we don't know how to do it, it's that people don't like the consequences of it.
Your bank can give you a bank card with cryptographic keys in it and then you need the card to make a transaction. But then if you lose the card...
At which point we fall back to birth certificates and things because there's nothing else available. The alternative would be that if you lose your bank card, you lose your money. Which could be mitigated by e.g. having backup cards that you keep at home in a safe, but some people would lose those too, and what then?
Why would losing your bank card mean losing your money? The bank card would be there to establish identity when performing a transaction. Going to a branch in person with government-issued photo id would be the way to establish identity when generating a bank card. Itβs a pain to do, but it only needs to be done for a new account or to revoke/replace a card.
By analogy, the cryptographic key on the bank card is a cross between a session token and a private key. Like a private key, it is never directly exposed for verification. Like a session token, it can be replaced.
At least walking into a bank with a fake birth certificate and other forged identty is not a form of impersonation that can be done remotely and at scale.
Your bank can give you a bank card with cryptographic keys in it and then you need the card to make a transaction. But then if you lose the card...
At which point we fall back to birth certificates and things because there's nothing else available. The alternative would be that if you lose your bank card, you lose your money. Which could be mitigated by e.g. having backup cards that you keep at home in a safe, but some people would lose those too, and what then?