Honestly, the shortest solution to these problems would be to reshape the law so that banks are 100% responsible for fraud. As in, if they open an account tied to somebody and it turns out to be tied to somebody else? 100% on them, the person who they were deceived into believing they were doing business with is fully protected by the law from any ramifications.
Of course, this would completely change the risk model banks operate under and fundamentally reshape commerce as we know it. Thanks would become hypersensitive, all business would be conducted in person, banks would reserve the right to tie up your money for years if you couldn't prove who you were (think getting your Google account unlocked when Google suspects fraud, except now it's your money in the bank down the street...).
SSN is voluntary. If parents would stop opting-in their babies into this data scheme, Americans could grow up without these numbers.
After ominous threats about 'must choose name for baby' my wife and I left the hospital with our baby. Health insurer sent new member card with name 'baby girl' which worked great for all the follow-ups. And nobody from big government forced me to apply for SSN. We did get a passport (SSN on that application is optional) and travelled internationally before the first birthday.
Most of this nonsense data collection is voluntary. More and more in life I say "No thank you" and move on. Many Americans get a warm blanket feeling by putting their children into voluntary data schemes.
You are going to get a lot of people telling you that you're a libertarian nutjob. Even here, which touts itself as a bastion of internet privacy champions and "experts".
But you, you're walking the walk. Asking the hard questions and accepting the consequences. There is only one way to make things change.
Don't let any little pedants tell you "how your daughter is going to grow up", either. Or that they somehow know how she'll feel about you.
FWIW: my kids have SSN's and that is just as dangerous as what you've chose.
Employer is required to verify citizen or immigration status. For an American with a passport, the passport works okay.
Passport works great for ID all around, because it does not require SSN and does not have home address.
Many things, like TSA (Soviet era) checkpoints don't actually require ID. People seemingly prefer to act like cattle and show IDs everywhere and voluntarily consent to full body scans. Then people complain that their bits of privacy got leaked. Of course it leaked, and you voluntarily consented.
Elsewhere in this thread you're talking about birth certificates being voluntary (they're not). How are you proving citizenship for your passport without one?
No, the banks haven't, which means you haven't, bucko.