The government only claimed to identify you with that number for one purpose. The motivation for fraud would be a lot lower if that was the way it was still.
The problem is third parties abused that number for their own purposes.
Imagine if some company somewhere started using phone numbers as identifiers, and criminals started defrauding that company by "stealing" other people's phone numbers. Would you blame the phone company for that? Of course not.
The problem is that banks and anyone else using SSNs need to do more due diligence than checking SSNs, but they don't want to because it would be expensive and add friction to signing up for their "products".
They themselves abused it as anyone in military service is well aware. Then they required you to put it on your IRS forms, even though the Social Security Administration is a wholly independent agency. Then they required banks to capture it for any customer.
It goes on.. third parties weren't the worst and they didn't start it and some are required by law.
Imagine if Credit Card companies were as blatantly incompetent and as reckless as the government? The reason they aren't is because they hold most of the liability at all times, and there's a lot of good laws that set them up for huge damages if the make a mistake. The reason the government doesn't care is because no one holds them accountable.
If you have an interest bearing account, you need to provide an SSN, and even though the regulation has since been changed, you needed it for any account for 30 years or so. Anyways, if my SSN suddenly starts being used 12 states away from where it has been the last few decades, _nobody_ notices. The government is the only agency that could and they just don't.
It seldom creates significant inconvenience or financial obligations when someone pays additional taxes in your name. It only becomes a significant problem when the fraudster is obtaining money or services in your name.
The burden of authentication is not on the entity who issued a simple ID number, it is on those who go on to use it as if it is a secret.
I think your trust in credit card companies is misplaced. The only thing that holds them back is consumer protection laws, and they fight those however they can. Jack up rates, check. Grant credit at a sales point of presence with a minimum wage sales clerk doing identification, check. Sell or trade your payment history, check.
In some moral systems, lending money to make money itself is outright wrong. If you maintain a balance on your credit card for day to day expenses, any financial advisor will tell you to stop that.
The problem is third parties abused that number for their own purposes.
Imagine if some company somewhere started using phone numbers as identifiers, and criminals started defrauding that company by "stealing" other people's phone numbers. Would you blame the phone company for that? Of course not.
The problem is that banks and anyone else using SSNs need to do more due diligence than checking SSNs, but they don't want to because it would be expensive and add friction to signing up for their "products".