The entire problem is that people started using SSN as a shared secret, but it was classic password reuse. Use the same secret every fucking where.
No. If you want to establish trust, use a random secret for each new trust relationship.
If you want to establish identity ask the identity providers what kind of anti-forgery guarantees they provide. Oh, nothing, you say!? Then don't use that provider.
Banks are trying to use easy to forge things to make sure they won't lose money. Sounds like stupidity. So they limit their stupidity (hence you can't just register for a credit card online, otherwise bored Russian teenagers would have already bankrupted them).
They shouldn't even ask for it.
Currently fraud is held back by law enforcement. Which is triggered by fraud detection. Which is triggered when the wrong person gets a call from a collections agency.
And this chain of events is too long, but since there's no global (national) system to check if someone is a professional scam artist or a regular bloke, that's what banks are left with.
Of course the government will never let a good crisis go to waste. Instead, we will all get chips under our skin that can't be removed that will be passively scanned by the authorities everywhere we go.