So far only PCR tests are available at scale. Those PCR tests are very sensitive (e.g when detecting traces of long broken virus on surfaces) but even they are

So far only PCR tests are available at scale. Those PCR tests are very sensitive (e.g when detecting traces of long broken virus on surfaces) but even they are only reliably positive for a few days into the infecting. Apparently, the immune system wins the battle for the upper throat quite easily, even in patients who later die from pneumonia. If you did a random sample study with a test that only identifies a positive for a short time you'd still have a huge uncertainty from not knowing reliable averages about how long someone infected "lights up" in the test. There just isn't much information upside from background sampling PCR, particularly when serological tests (those than detect who already had the virus) will soon be available. Those are not useful at all to combat spread anyways, so they can be used for background testing without competing for more immediate use cases.