"COVID Cases" turns out to be anyone with covid who might be in the hospital for anything else. COVID deaths have included people "greedily" the same way. Shouldn't the vaccine be counted by the same standards and the same statistical methods used?
Comparing Covid statistics to VAERS is comparing apples to oranges.
I completely reject your premise that the covid statistics are shoddy. It's easy to confirm a covid case. You do a PCR test, and if you get a positive back it's covid, end of story. It's admittedly a bit trickier to attribute a covid death... but not really. If a covid patient dies of a heart attack, it could be bad luck, or it could be the disease that coagulates its victims' blood. But usually it's pretty obvious. Someone dying of pneumonia and/or a cytokine storm isn't exactly subtle. There's nothing in the overall death statistics that suggest that the obvious covid deaths are anything but the obvious.
By comparison, establishing a casual connection between a vaccine and any adverse side effects is incredibly difficult, simply because they're so rare. Of the 44000 people in the Pfizer trials, literally none of them died of covid OR the vaccine, vs 15 covid deaths in the unvaccinated control group. And VAERS is just a safety net in case something small-but serious slips through the statistical power of a full scientific study (as happened with the J&J vaccine).
I fail to see how this is relevant. Obviously some set of people will test positive after they've been hospitalized for other causes, and another set will have mild cases that don't progress to the serious your-lungs-no-longer-work stage. The total cases and hospitalizations are still good general metrics to gauge the severity of the crisis and balance risks. If statistics didn't have nuances we wouldn't need statisticians.
Regardless, your objection is irrelevant to the comparison you've tried to make with VAERS. The COVID statistics are a sweeping accounting of common, obvious events that are easy to verify. VAERS, by contrast, is designed for hinting at the sort of literal one-in-a-millon range events that controlled medical trials can sometimes miss, where determining cause and effect is difficult. They're different tools for different jobs. Trying to apply standards from one to the other is simply spurious.