Interestingly, the Israelis are finding the effectiveness of Pfizer to be around 40% effective at preventing symptomatic infection. So what constitutes "high viral load" above, likely is a full blown flu (ILI) condition. One is probably still fairly contagious with milder symptomatic conditions, such as one would have with a contained cold (sore throat followed by some mucus and moderate nasal congestion). If milder contained conditions like this is accompanied by a cough, then one is highly contagious during coughing (this is when most of the viral shedding and dispersal happens). For the vanilla varieties of the SARS2, dry cough was a common (perhaps universal) symptom. Thus, effectiveness as far as spreading potential likely is around 40%.

When you read the study on breakthrough cases among SE asian healthcare workers, you see they tracked viral loads carefully over time. They found that viral loads peaked about 3 days after symptom onset. Almost certainly, the peak of shedding happens shortly (maybe a few days) after the peak viral load, so perhaps 5-6 days after symptom onset. Follow pdf link from this link to see study.

Given that a majority of the US population (I've heard numbers as high as 80%) are insufficient (should be reclassified as deficient) for levels of vitamin D, the far greater effect and much more low hanging fruit would be to have widespread vitamin D testing and supplementation. Even if this number is seasonally lower than 80% during summer and early fall, when you also account for insufficiency in other important immune nutrients, such as vitamin C, you will reach a number very close to 80%.

When you then consider that underprivileged communities, one even finds that this number, 80%, is probably greatly lowballing "insufficiencies". If they're going to be going around trolling these neighborhoods for more test subjects, they should also be trolling for vit D testing and handing out C+D immune supplements.