Earlier quoted context omitted.
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Why are you drawing an equivalence between a test for a contagious disease and a genetic analysis service like 23andme? That seems a bit extreme.
I'd not have a problem with an employer offering daily on-site testing with no persistent logging for people who have to be on-site but for whatever reason can't be vaccinated, or if they're having outbreak problems in the area.
If no one stored it, there would be nothing to get leaked when the eventuality of data breach happens. Storing it is not in the best interest of the person taking the test, is it? Doubly so for negative or inconclusive results.