Surplus deaths (deaths now minus average deaths at this time of year, for a given time period) is probably the least worst measure to get a grip on what's actually happening. But even those figures are likely to be wrong, particularly in badly affected areas, simply because coroners, doctors, and other officials who handle deaths, have far more important things to do than collect and report statistics for the bureaucrats.
Dead bodies have procedures that are applied to them,
few will slip through the cracks.
This is not accurate. Most bodies do not have or need to have autopsies performed. In my state, any body found unattended is automatically autopsied but otherwise, cause of death is almost always already established as most people die in a medical setting. Autopsies are performed only when the cause of death is unknown or if there is some other kind of investigation being conducted, such as a criminal investigation or if for some reason, an insurance company wants one or perhaps the family if they wish to dispute the presumptive cause of death.
Medical facilities are being overwhelmed with cases of COVID 19. Bodies are piling up. There are reports of mass graves. Do you really think that there are enough coroners or medical examiners to handle the number of deaths due to presumptive COVID 19? There simply are not, nor are there places to store bodies until samples can be collected tested and an autopsy can be conducted. Not to mention the risk of exposure to any person handling the body (yes, I know the virus is not known to be transmitted via blood but there are a lot of body fluids that are not blood).
There are rumors/reports that deaths due to COVID 19 are not being properly counted--either being vastly undercounted or vastly over counted, depending on situation and news source/political hay to be made.