I would venture to guess that the number of those this passed through silently is staggeringly high, as is the count of those who died without testing because "the test wouldn't affect the treatment or outcome" (I've personally heard this before, it's a medical go to and as annoying as ). When we see the number of cases written about and consider than many states, like Pennsylvania, will only test with a Dr note that means a whole lot of people are uncounted so the count is going to absolutely be wrong. It would be different if the tests were on demand but that ship has sailed, there is no reason at all to think our count is accurate. A better statement would be, "Here is the number of people who can afford a Dr. visit and have a Dr. willing to fight for them who were tested and came back positive (or negative)." The obstacles in play can't be ignored.
On the other hand, I'd bet that most of the high touch essential workforce, especially in bigger cities, have had it pass through their population silently already thanks to the mask controversy so maybe a tandem effort of antibody testing plus vaccination would work in this group. It's ok if the self generated antibodies don't last forever, we don't need forever we only need until there is more so if there is a combination of vaccine and herd immunity to get us there so be it. If you antibody test a whole bus depot now and discover 50 workers are positive for antibodies, save those 50 doses of vaccine and redistribute elsewhere to extend coverage into another community. It's not an impossible problem to solve, this is a public health emergency, time to use whatever resources we have at our disposal to cover as much vulnerability as possible without wasting a single dose.