There's a logical inconsistency here. If we assume that the total number of cases is much higher than reported, then the hospitalization rate per infection is d

There's a logical inconsistency here. If we assume that the total number of cases is much higher than reported, then the hospitalization rate per infection is driven down by the larger denominator. There's a point at which there are so many total cases that the number of hospitalizations is problematic and noticeable. If we continue to assume that the total number of cases is much higher than reported, the death rate per infection (IFR) is also driven down by the larger denominator.