For the hospitalization ratio we don't have enough testing in many places but for those countries that are successfully pursuing test and trace strategies we can be pretty sure they're at least discovering the majority of contagious infections. So we can guess at the rough number even if we don't have it nailed down precisely.
Iceland is leading testing rates at almost 146 per 1,000 people[1]. This is extremely low for a hyper-contagious pathogen like COVID-19. No one is "pretty sure they're at least discovering the majority of contagious infections" -- let's call a spade a spade and build models that actually make sense.
If you use contact tracing to find out who sick people interacted with you only need to test those people rather than everyone and you can get by with far less testing overall. Then it's about the number of tests per case rather than the number of tests per capita. The percent positive rate on tests is a very important metric there as well and it seems that countries that control the spread get that down far enough that false positives outnumber true positives.
This kind of mental gymnastics just muddies the waters. My original point was that hospitalization (and/or ICU) rates are contingent on infection rates and that no one has reliable (and/or accurate) infection rates. Exactly how you calculate infection rates (testing, contact tracing, self-reporting) is immaterial.
