This is probably the best answer. A birth certificate is just one more document in a long list of evidence that Jim Smith of 123 Main St. exists and you are him.
What the BC does is prove that there is an actual Jim Smith, and he was born at time X in location Y. Given more modern ceritificates issued on more secure paper, and correlated with database entries, it makes things more secure. Hence the PR dilemma - a birth certificate could be totally invalid as in containing data that is not true, so make people obtain a new one. Now, a new (valid) BC at least relates to one real person’s birth.
There are a limited number of people. If you start with the presumption “this is Jim Smith” then if 2 people try to claim they are the same person (based on BC) that can set off flags. So it makes it harder to fabricate a name and birth. If you must then impersonate someone, the trick is not getting caught as a duplicate.
The “dead baby” technique (as made famous in the original Day of the Jackal) might have worked once, but more and more, birth and death are correlated in databases to eliminate this option.
The next step is additional ID, the “paper trail”. The DMV can ask for a birth certificate - that does not prove who you are, but it links you to one particular legitimate birth. Person A belongs to drivers license for A. If two people appear to be the same person - different addresses, pictures, etc - that sets off alarms. If you cannot create a fraudulent BC, if you can’t use a dead person, you can’t avoid the “duplicate” problem.
Throw in supporting paper trail - SSN, employment history, school records, etc. The SSN is tied to a birth record. It also must have a history of tax records tied to it. (note the other difficulty - if you hire on with Jim Smith’s SSN, your employer will remit your taxes on that SSN. Eventually the IRS will note that oddly, Jim Smith is working two places at once, either submitting two different tax returns or failing to declare half his earnings.
And so on… You can dream up a dozen easy ways to bypass this for a good crime novel. They typical one, find someone who won’t be missed, murder them, hide the body, move far far away where nobody they knew will meet you, and assume his identity. Avoids the lack of paper trail and possible duplicate issue.
The birth certificate itself proves nothing, but forces you to tie your claim of identity to a specific person born at a specific place and time. It makes it that much more difficult to fabricate an identity out of thin air.
And, since the quote was from the thread on the effect of ID laws on poor people and elderl, and identification for votingy - note that people on the fringes of economic life, with a minimum of accumulated documentation still in their possession, no money and no computer - will have a much more difficult time establishing the necessary paper trail to validate their identity.