That sounds like the perfect way for a disease to spread. Do nothing to most.
I live in Hungary, where health care workers don't get (enough) protective wear, the health care system is neglected since decades, and government is not willing to communicate clearly. Also, most of the people who should be tested are not tested, because of the "protocol".
I fear this, and the rate of asymptomatic cases will lead to a deadly mixture here.
It was done with students who took flu vaccine. They found people socialised more after they had the vaccine (and thus, were a little bit infected) compared to before.
A literature review looked at the study and came up with the negative explanation - that people felt more secure or relaxed after getting the vaccine as they felt safer. Or were more nervous about needles before.
Ancedote:
I think I have covid-19 and the days before symptoms I felt unusually anxious to get outside and amongst fellow humans. I'm usually an introvert and stay inside mostly so it was notable.
Suggestion:
Online interview people with symptoms now to collect data on peoples behaviour in the days before symptoms showed, when they were infected but not showing, compared to 2 weeks before.
Basically, the most successful viruses—colds and Norwalk like viruses—modify our behaviour by hijacking one of our body's defence mechanisms so that they can spread more easily.
I would guess that the mildest form of disease sufficient for such behaviour changes would probably be the best strategy. This would keep the infected host active enough to circulate and spread the virus.
My layman's opinion on covid is that it will become weaker the more it spreads through the population, to the point that when most of us inevitably get it it will cause symptoms like a cold or mild flu.