The SSN is not an ID but a number: anyone with your number can claim to be you for the purposes of transactions. The number is only tied to name and birthdate, maybe address if you are of the age to pay taxes. This enables a lot of fraud: I once saw someone apply for a rewards (credit) card in a US store with SSN and no photo ID ("Oh I left my drivers license at home, could you take a student ID?")

Not sure how Europe handles this, but here in Korea phone numbers are tied to government-issued photo IDs. Sellers of phones have to fax ID scans to the central office for verification. Remote transactions such as signing up for a credit card require phone name + first half of ID + phone number 2FA at a minimum.

As a result, I'm not aware of any cases of identity theft. US infrastructure is so broken.