This is completely contrary to what "excess death" statistics suggest, which is that we might be under-counting COVID deaths by quite a bit. We've had many more unexpected excess deaths in 2020 and 2021 than can be explained by the official COVID death counts, so it's highly possible that some COVID-caused deaths aren't being recorded as such.

It could be that a bit more than 625,000 people have died in the US due to COVID. Or it could be higher than that, and it may be a couple of years before we know for sure. It's not lower, though. Not at all.