If there are still test shortages and the hypothetical dad has no symptoms, why should he be tested? Hopefully at some point everyone will be. I still think the best guidance is to stay home and isolated once symptoms start until things are bad enough to warrant a hospital stay. Cuts down on the exposure to our healthcare workers and limits their work to only those that really need it and are not just curious.

Those who don't have it and are tested have just unnecessarily exposed themselves to risk. I would imagine that almost everyone tested has some sort of symptom and believes they have it and yet they are overwhelmingly wrong in every state. So logically your scenario might make someone paranoid about getting it but that is not evidence and certainly not as much as those with symptoms, who are also overwhelmingly wrong about having COVID