I 100% agree that we should be running antibody tests to see how many people have caught COVID-19 and recovered. All of our testing until recently was based on RNA tests, which may only be positive during a relatively short window. (I saw a case study claiming that even some hospitalized patients are testing negative inside 7 days.) We need to know how many people catch this and beat it quickly.
That said, even in populations that have been RNA-tested early and extensively (such as the Diamond Princess and South Korea), the number of completely asymptomatic cases is less than 50%. Using the most optimistic data, I personally have less than a 0.5% chance of dying assuming I get all the medical care I need.
And that's the problem. This virus hospitalizes about 20% of identified cases. They require some supplemental oxygen, and maybe an IV. With good care, probably less than 1% die.
So there are really two key fatality rates:
1. How many people die if they get all the care they need, and
2. How many people die if 30+% of the population catches this at the same time?
Even if we're overestimating (1) by a factor of 10, that's still enough to make (2) catastrophic. What happened in Wuhan and Lombardy can happen here, and there's absolutely no reason that it couldn't get 10x worse. Even if we're overestimating the disease.
So let's start testing aggressively for antibodies. Until we get that number, I'm all for extreme caution.