I suppose it is possible that the majority of people had no symptoms or reason to be tested, but that's because those folks are idiots. In contrast, there was *a lot* of testing, and still is, for people who know they were exposed to someone who has tested positive, or who are showing symptoms themselves.

It's true that the moment you walk out of the test center you could *then* be exposed. No one doubts that. The point was to make sure you didn't get it from the known exposure, or the symptoms you have. That's incomplete, but it addresses a specific need.