Thanks Tim for a clearly-reasoned article. Ironically I'd say that you also illustrate, perhaps unintentionally, some of the other dangers of what may be termed "naive" statistical analysis. For example, if we adjust data to account for pattern over time, the States that are now showing increases in both reported cases and mortality rates seem to fit the classic "early 2 phases" of the pandemic, after which pretty much every place experiences a steep and continuous decline with only tiny blips here and there to interrupt the long tail down to zero deaths. And in these "long tails" it's apparent that infection rates and mortality rates are largely decoupled. France, Switzerland, Netherlands, et al all evince this clearly.
The reasons for such a trend lie outside statistics entirely, and thus stats can't explain the trend. Once we realize that (a) many less-serious pandemics (such as flu) take the old & weak and then tail off because most of the rest of the population is more resilient, and (b) doctors have now largely abandoned the practice of inducing comas and intubating patients (which killed an estimated 70% of those unfortunate enough to experience such interventions) we can see that "naive" predictions of a hard correlation between infection rate and mortality rate over several months will produce misleading assumptions.