It is this, and this alone: find COVID-positive individuals that are willing to volunteer to be traced. Prepare legal assurances that they will not be imprisoned for revealing their positive status. Trace their contacts, providing the same assurances to them. Find the rate of transmission for asymptomatic, as well as symptomatic, carriers. This would be a strictly delimited experiment to ascertain the character of the virus, and how it spreads. It would not be an open-ended, endless war on a virus.
In fact, this has already been done in several cases. This asymptomatic woman was contact-traced. The 455 people she came into contact with never developed COVID symptoms, meaning that asymptomatics do not transmit the virus.
There are other examples. The point is, contact tracing of select individuals is possible, as long as their consent is obtained. No harassment needed, no massive domestic army of snoops and snitches. Of course that would be too easy. Government doesn’t like a plan with no room for mission creep.