One way to achieve ubiquitous screening is for people to perform regular VO2max tests (loosely speaking; you can do submaximal exercises for this). You quickly figure out if you have a stress on your immune system (by watching various metrics), and there are sports-science papers showing this (because they use it to avoid overtraining, which also appears as a stress on the immune system). This is of course not easy to achieve with our current culture. It used to be that physical achievement was valued. Only a small fraction of society pushes against their VO2max in a regular way that can be measured and tracked to detect the immune-system stress. If people were to pursue this approach, they'd become a lot healthier in general.
This seems like something that would detect symptomatic patients only, I haven't heard of any research showing that patients would see lowered oxygen saturation in the early stages of infection.
So for people who are going to get sick it would trigger too late, letting them spread the infection for days until this test catches it; and all the many infected people who will never develop any symptoms (perhaps up to a half of infected according to the Iceland tests?) would never 'fail' this test, but still go on infecting other people.
You wouldn't pay attention to oxygen saturation, and I'm not sure if you can even use that as a metric. Generally this involves heart-rate variability, heart-rate recovery, etc. This detects the stress on the immune system, which is detectable soon after your body starts dealing with an illness. If the asymptomatic case has a stress on the immune system, which it likely does, then this test will detect it (so it actually isn't asymptomatic in a strict sense). It won't be able to tell you that it is Covid 19, but it can be used as guidance to behave as if you have the asymptomatic case. You could even just look at your performance: a significant drop in output means your body is unhappy about something. Imagine running/biking/swimming/etc at full capacity when you have a cold: you can't.
