>> First, they are driven significantly by amount of testing.

That depends which numbers you follow. "Cases" is different than "clinical cases". A clinical case will show some sort of symptom. While asymptomatic spread is almost certainly a thing, symptomatic patients spread much more readily than asymptomatic. So rather than look only a total cases, look for data on clinical cases because those are the ones that are most likely to spread to others. That will normally be patients under treatment rather than the larger number of people who have tested positive, show no real symptoms, and are sitting at home waiting for another test.