The use of "counting new cases" in my comment #266 came from Dr Fauci in minute 1 of the following video:
Do you mind citing a reference or video from a reputable source of using the "number of deaths" as better data to use?
I think your two positions can be harmonized. Dr. Fauci says we can know if we have turned the corner when the number of "new infections" stabilizes. New infections are determined by the native infectiousness of the virus, the efficacy of our social isolation countermeasures, and (eventually) by the presence of herd immunity.
The problem is that the number of "new positive results" likely is
not equal to the number of "new infections". In fact, at this point it is likely to be higher due to the rollout of more and better testing. Actual infections may not be going up while positive results may still be climbing. That is, you can have exactly the same number of infections yesterday as you did today (i.e - zero new) but if you test more people today than you did yesterday, you will show more positive results, because you missed some yesterday.
If instead you use deaths from COVID-19 as your measure, that is unlikely to be substantially impacted by improvements in the testing regime. It is a lagging indicator, to be sure, because people who ultimately are going to die will linger in the hospital for some time before succumbing to the virus. But I think at this point it is probably more accurate.
As I have noted before, if the hospitals become overwhelmed, more people may die from simple lack of treatment and using deaths as the measure could become inaccurate. Additionally, if some of the new therapeutic measures (e.g. chloraquine) prove to work, then the death rate will change and may not accurately reflect the number of new infections. Similarly, if we reach the point of widespread, rapid, and accurate testing, such that the number of new positives really is equal to the actual number of new infections, then we may want to reconsider using the number of deaths as a lagging proxy.
I don't have any particular video or article to point you to, but thinking hard about this has led me to the conclusion above.