That is exactly right, and exactly how adopted and donor-conceived people are using the consumer DNA testing sites.
If you’re responsible for that many offspring, either you yourself made unethical choices or you didn’t do appropriate vetting before choosing a particular company that made unethical choices with your genetic material.
I find it incomprehensible myself(outside of considerations like “family history of X” where data about the donor is obviously relevant); but given the massive interest in things like genealogy; and people using affectively charged terms like “heritage” for “stuff dead strangers a continent away did 500 years ago, if I share some DNA with them; but only then”; it’s hard to escape the conclusion that it’s a big deal in many eyes.
What I find interesting in the UK case is that; while the law doesn’t merely note the difficulty of concealing genetic data given today’s technology; but actively forbids anonymity for UK donors; it is nevertheless legal to source anonymous sperm from offshore(and, given the supply problems, relatively standard). This has the obvious pragmatic value of making it possible to get donor sperm in the UK; but seems questionably consistent as a matter of principle.
If the perceived interests of the child demand identifiable donors, why is it licit to use anonymous donor sperm? Do would-be parents outrank children; but children outrank donors? Is it just pure pragmatism without even a nod to principled justification?