I assure you, no one buying a pregnancy test wants an anonymous corporation or the government to be informed of the results. This has nothing to do with technological feasibility and everything to do with privacy concerns.
Your definition of reasonable seems to be pretty warped. The historical abuses of "this opinion is reasonable and scientific" are too heinous and numerous to even list. Thankfully we have (but still need more) consumer privacy laws.
No ones wants it. And yet if it comes out positive and you visit the doctor to confirm, it is known to an anonymous corporation, sometimes multiple, and government, if it cares. And everybody is perfectly fine with that.
Historical abuses are vast and many in all the fields of human culture. Proportionally to the power of given part of the culture. Abuses don't automatically make given thing completely worthless. Historical abuses are just things that we need to be on the lookout for.
Your definition of reasonable seems to be pretty warped. The historical abuses of "this opinion is reasonable and scientific" are too heinous and numerous to even list. Thankfully we have (but still need more) consumer privacy laws.