For a patient, a high false negative rate is usually worse. For an insurer, a high false positive rate is usually worse. The perspective matters.
At an individual level, false negative seems more dangerous. But at a macro level, a high false positive rate could lead to taking dramatically policy decisions
I agree with the caveat that false negative rate is much more relevant for society when a disease is very contagious. Take measles, with an R0 in the teens. A high false negative rate can cause explosive growth in the numbers of people catching the disease, which I think is what makes it relevant to the COVID-19 scenario
Implementation examples: South Dakota and Sweden.
It seems clear that the infection rate has been severely under counted, meaning mortality rates are artificially high. Even better (from the standpoint of restarting) that "flu-like" mortality rate is concentrated in people over 60 years old.
What that all means together is the economy can easily restart, with the most vulnerable (old and sick) taking extra precautions.
This entire thing has been a fascinating exercise in how poorly central planning can work given bad information. The cure has been vastly more damaging than the disease.
https://www.medpagetoday.com/infectiousdisease/covid19/85717...
Besides, the article you pointed down in a reply is about a different kind of test.
I do disagree that a false negative rate is not important in the context of a disease where asymptotic cases may still be contagious, however.