> The original purpose of the SSN was to enable the Social Security Board to maintain accurate records of the earnings of individuals who worked in jobs covered under the Social Security program. The card was never intended to serve as a personal identification document—that is, it does not establish that the person presenting the card is actually the person whose name and SSN appear on the card.

https://www.ssa.gov/policy/docs/ssb/v69n2/v69n2p55.html

So maybe there does need to be a federal or state identification method, but because we lack a legitimate method it should also be the responsibility of the individual to do due diligence that the person they're giving credit to is the person they say they are.