No doubt there's an under count of total cases. I admitted as much. But we're making guesses about how much of an under count.
The conspiracy theories about significant over count of deaths really irritates me. Because it's based on anecdote and, quite frankly, a misunderstanding of how causes of death are determined. Like let's say I've got hemophilia and get a nasty cut. A perfectly healthy person would live through it, but I bleed out and die. What's my cause of death? It's reasonable to say laceration and blood loss, because that's technically accurate, but it was the hemophilia that killed me. Or let's say I'm in a motorcycle crash and break some ribs, makes it hard to breathe but is otherwise recoverable. But during my recovery I catch COVID and die. Why did I die? Was it the motorcycle accident? To the extent that it affected my ability to breathe yes, but it would be an accurate statement but for the onset of COVID pneumonia I would have lived and THAT is a legitimate cause of death. Another example would be to ask how many people you know that have died of cancer. My father in law died last year after a battle with leukemia. But he technically died of pneumonia while he was fighting. But labeling his death as cancer caused is accurate and not fudging the numbers.
All you have to do to see that we're actually under counting COVID deaths is go to the CDC page for excess deaths in the USA. These people watch this kind of thing. They have a pretty good idea (within a margin of error) how many people are going to die in the country week-to-week. It's pretty consistent. In 2020, the USA has over 200,000 excess deaths from what would be normally expected. That's a lot closer to the real death toll.
A final consideration we should all think about is how much better our treatment is today than in March because the doctors have learned so much about how to treat. We're averaging like 1,300 deaths/day now. At our worst it was about 2,500. I would argue that if we were still using the care used in March, that 1,300 figure would certainly be higher, maybe as high as 2,000/day total. But regardless of how many hundreds more per day that they're saving, that's hundreds more that are pulling through after a serious hospitalization and with unknown long term effects.
Like many things in life, this stuff is complicated and there are no easy answers.