The current way things are being counted is how health experts and departments around the world have counted deaths in previous epidemics and how they're counting this pandemic.
Just as with previous epidemics, we won't know the real toll until in-depth studies are done a few years down the road. That's how we arrive at things like "12k deaths from swine flu," after the fact epidemiological studies and surveys which are themselves estimates rather than just hard counts of death certificates.
If the WH gets their way, we're going to see the media mainly reference the politically suppressed "official" death counts that don't include any of the nuance you're mentioning. It'll just be "oh only 80k people ever died, no big deal, everything else is a conspiracy." You've already seen it pop up in this thread today!
It's not the medical experts pushing for this change for more detailed information. It's an extremely political White House doing it for very obvious reasons. Don't make excuses for them.