Good idea in theory, not so much in practice, especially over longer periods of time. First, people are fallible and many of them who don’t know if they have it or not, may not take it seriously. Having a positive test (even if asymptomatic right now) would put them in a different mindset. The ability of quickly confirm recovery would put the people in critical roles back to their occupation. Medical professionals, police, truck drivers, water treatment plant workers, utility workers are all going to get sick in droves and it is not going to be pretty.