Two women mistakenly issued the same Social Security number

This wouldn't happen if US had something like Estonia's system:

> The Estonian identity card (Estonian: ID-kaart) is a mandatory identity document for citizens of Estonia. In addition to regular identification of a person, an ID-card can also be used for establishing one's identity in electronic environment and for giving one's digital signature. Within Europe (except Belarus, Russia, Ukraine and United Kingdom)[2][1] as well as French overseas territories and Georgia, the Estonian ID Card can be used by the citizens of Estonia as a travel document.

> The mandatory identity document of a citizen of the European Union is also an identity card, also known as an ID card. The Estonian ID Card can be used to cross the Estonian border, however Estonian authorities cannot guarantee that other EU member states will accept the card as a travel document.[3]

https://en.wikipedia.org/wiki/Estonian_identity_card

This also happened in Turkey on a massive scale. When the government implemented the 11-digit national identity numbers for the first time in early 2000s, there have been thousands of cases where the same ID number was given to the multiple people, and also many other citizens with no ID number.

Some reported that it was due to the ID number field in database not being a primary/unique key in database. The leaked Turkish citizenship database also confirms this, although we don't know if that leak reflects the original database structure.

> “The officer told me that talking about this Social Security number mix-up could result in delaying the green card process that could be done in six months to 2-3 years,” she said.

U.S. gov't makes a mistake and it is still somehow your problem.

> “Sounds like a glitch, maybe human error. The error rate is pretty low — they’ve issued 450 million cards.”

No. Mistakes are not an option no matter the scale.