That wasn't the claim. The claim was that an unvaccinated person can self-isolate when they observe symptoms.
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 a vaccinated person
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?
The problem with COVID-19 all along has been that it is transmissible before being symptomatic. That is why it spread like wildfire when SARS and MERS did not. Listened to a good interview on NPR some months ago with a leading coronavirus expert who went over this in detail, but unfortunately can't remember her name or find the interview right now.
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.