Not sure what you want me to look at on the Wikipedia article was it this?
However, there have been instances where multiple individuals have been inadvertently assigned the same Social Security number
The reference actually only mentions a single instance of this happening, not multiple as the Wikipedia article says. Yes, that was a case of two people being assigned the same number. However, they also had the same name and same birthday, so your assertion that the federal government uses a combination of SSN and birthdate wouldn't do anything in that instance.
The second and third citation you provided are just the hysterical news stories brought on by the ID Analytics (LifeLock) study that I already mentioned. That study found nothing about people being issued duplicate numbers or that SSNs are not unique. None of the citations show any support for what you said:
SSNs are not unique. Many people share SSNs with other people that they have never met, and may not even be aware of. What is unique is the SSN+DOB combination. That is why any government form that asks for your SSN, will also ask for your DOB.
You've shown that there is at least one instance where two people were issued the same number (which was fixed), but shown no evidence that SSNs are not unique or that the purpose of the government asking for your DOB is that they use a DOB+SSN combination. The government doesn't (knowingly) issue the same number to multiple people. You claim "many people share SSNs" but that's not the case. That's like saying "many people share credit card numbers" because sometimes people use other people's credit card numbers for fraud. It's just not accurate.