The ideal in question isn’t “at birth”, it’s whatever it is that drives folk to think “at birth” somehow matters more than “now”
If that's the point you want to argue, you'll have to go find somebody who holds that ideal, which means someone other than me.
My point is and always has been very simple - a birth certificate is a just that - a record that on some specific date at some specific time, a baby was born to some specific person. That's it. That's all it is.
That doesn't mean or even imply that "'at birth' matters more than 'now'." It means that a birth certificate has one and only one job - to record a birth - and anything and everything after that is some other document's job.
And in fact, I would say it's undeniable that "now" is more important than "at birth," which, again, is exactly why the very first thing I said was that, to me, the whole issue is an argument against using, or requiring, a birth certificate for ID.
To me, it's as if you're arguing that a doorbell should also be a microwave oven, and when I point out that a doorbell's job is to be a doorbell, you accuse me of holding the "ideal" that doorbells are more important than microwave ovens.