At the same time, it's completely misleading to report all of these deaths as unambiguously COVID deaths, because they weren't. Many of these people would've died from almost any infection. Many would've died without any infection at all.

This isn't the approach that folks normally take. If a family member has severe heart disease and one day they get the flu and die, sure, they can get counted as a death due to the flu and you can understand the flu as technically having dealt the deathblow. But everyone knows that it was severe heart disease which was their undoing, including their doctors. The difference between the flu and COVID is that with the latter we have a huge national media apparatus trying to inflate the number of COVID deaths as much as possible, completely ignoring all involved complications.