As the CDC said above, absence of symptoms is not a sufficient indicator for a vaccinated person. If a vaccinated person is tested regularly, they can self-isolate upon a positive test result, since they can't rely on symptoms as a signal.
Absence of symptoms is not a sufficient indicator for the unvaxed either, so your argument falls apart.
Why isn't 90% reduction in ICU occupation and 70% reduction in chance of infection a sufficient argument for the public benefits? Just because it is not perfect, you'd rather let the country's hospitals overload and shut down?
In any case, vaccines don't really change the equation here. Testing for temperature and symptoms with COVID have proven to be ineffective because asymptomatic transmission in the early stages is a thing with COVID-19 even without vaccination.