You don't need to capture every persons DNA for that. I'm not sure what the numbers are, but I presume there's quite a few without children at all. You also

You don't need to capture every persons DNA for that. I'm not sure what the numbers are, but I presume there's quite a few without children at all. You also have no need to store the DNA after you've determined lineage. Who your parents are don't change later. So, a third party could perform individual verification in cases where required, and the DNA sequence itself could be destroyed afterwards by that same third party. No FBI database need exist for any of this.