absolutely not! we have had massive migrations both from India (after independence) and Afghanistan (after the russian occupation). This is NOT a given.
Things have NOT been easy... and in fact dare I say, our ID department is rather dumb and stupid. I personally have had MULTIPLE issues with them.
But we have been doing SOMETHING, and the fact that the US doesn't... is insane.
When a child is born, the parent has to get them registered at the local council office. And then when my first card was made at 18, my dad went with me as verification, he attested that I was child #X as per the family tree, they confirmed someone with my name was in that family tree in their records, and used that as verification for me.
If parents are not available they can use relatives, as long as there is a family tree link. Not sure how they do it otherwise, but there is some system for refugees etc too.
But yes, I agree, it is a pathetic problem for a 1st world country to have - just sort it out.