According to your hypothetical graph that shows positive cases going parabolic, that’s assuming the same rate of testing. Now we are testing exponentially more people whether they are symptomatic or not. In that case the graph should be going EXTREMELY parabolic but it’s not. It’s showing a steady incline despite testing exponentially more people, your hypothetical graph doesn’t account for that l. In my opinion we did flatten the curve, but a graph that doesn’t account for the number of people tested isn’t is obviously going to paint a different picture.
The theoretical scenario is discussing serious/fatal cases - those requiring hospitalization. Yes, the overall numbers include asymptomatic cases.
Then, in the scenario you describe, if we have way more asymptomatic tests, then we should have a much lower death rate per case than similar countries. In other words, if extra testing is simply doing a better job of revealing asymptomatic cases within the US vs other countries, we should have a much lower rate of death per million than those similar countries.
Here is the date for the top ten countries in terms of number of cases, comparing their death rates (per million), cases rate (per million), and the death rate per cases:
Country
Cases
Deaths/Million
Cases/Million
Deaths/Total Cases
United States
5,251,000
502
15,855
0.0317
Brazil
3,057,000
479
14,373
0.0333
India
2,267,000
33
1,641
0.0201
Russia
892,000
103
6,117
0.0168
South Africa
563,000
179
9,490
0.0189
Mexico
486,000
411
3,764
0.1092
Peru
478,000
638
14,476
0.0441
Colombia
398,000
258
7,805
0.0331
Chile
375,000
530
19,601
0.0270
Spain
370,000
611
7,915
0.0772
So, if the reason the US has so many more cases is because we find more asymptomatic cases vs the rest of the world (due to all the extra testing we do), we would then expect the US to have a lower Deaths/Total Cases ratio, since we would have more "benign" cases of coronavirus. Looking at the top 10 countries, and the US ranks 5th out of 10 countries. To me, this indicates that the US rate of asymptomatic detection is not particularly higher or lower than the rest of the world.
I would expect the US to have better health care, on average, than Brazil, India, Peru, Colombia, and Chile. Yet two of those countries have a lower rate of deaths per cases than the US, two have comparable levels to the US and one has a higher death rate.
India and Russia are both lower than the US, but I wonder if this is due to how they diagnosis the cause of death - perhaps they just say pneumonia and leave it at that. Before looking at this data I would have expected them to have higher death rates per cases than the US. It looks like Mexico is still in the early stages of testing - they only seem to test those that are seriously ill, thus the death rate that is currently 3x higher than the US. If Mexico starts to ramp up testing we will see if they start to fall more in line with the other countries.
The only "early outbreak" country on this list is Spain and their rate is also very high, although I would assume they are still doing a lot of testing. Their high death rate per case may be due to the fact that not much was known about treatment when they suffered through their outbreak. Something similar may have happened in NYC as well - we've seen much lower death rates per cases in the US since then, and I think, based on what we see above, it is not really due to some incredible increase in asymptomatic cases relative to serious/fatal cases.
My thought is the reality is diluted somewhat by the additional testing we do in the US - we are probably still missing some asymptomatic cases due to false negatives, which if they tested positive would lower the US rate some. At this time I don't think the number is significant, but it may be bigger than we think.