DMcG I think you attach a reliability to the cause of death on a certificate that simply does not exist. From the link:
Death certificates from 433 autopsied hospital patients were reviewed and matched against the results of post-mortem examinations. Significant discrepancies between the two documents were observed in 50% of patients. In 25%, the immediate cause of death was incorrectly stated on the certificate, having been assigned to a different organ system in the majority of those cases. In 33%, there was disagreement on major disease other than the immediate cause of death. In 9%, the death certificate was signed before the autopsy was performed. The extent of disagreement was largely independent of whether the certificate was signed before or after the autopsy. We conclude that: (1) there is a significant discrepancy between autopsy diagnoses and entries on death certificates; (2) disagreement is not due to unavailability of autopsy data at the time of completion of the certificate; (3) death certificates should be completed or amended utilizing data gained at autopsy.


https://www.ncbi.nlm.nih.gov/pubmed/1871957
"lthough confirmed cases are reliant on a positive laboratory confirmation of the COVID-19 test, a laboratory diagnosis may not be required for it to be listed as the cause of death. In the UK guidelines, for example, it makes clear that practitioners should complete death certificates to the best of their knowledge, stating that “if before death the patient had symptoms typical of COVID19 infection, but the test result has not been received, it would be satisfactory to give ‘COVID-19’ as the cause of death, and then share the test result when it becomes available. In the circumstances of there being no swab, it is satisfactory to apply clinical judgement.”

This means a positive COVID-19 test result is not required for a death to be registered as COVID-19. In some circumstances, depending on national guidelines, medical practitioners can record COVID-19 deaths if they think the signs and symptoms point towards this as the underlying cause."
https://ourworldindata.org/covid-deaths
It is nnot   a perfect world.