> A simple indicator (new cases / total cases) lets us see what various policies are achieving. Increasingly strict policies make for lower exponential growth, but it still remains exponential.

Growth is only (approximately) exponential at the beginning of the epidemic. It follows the sigmoidal curve, which looks exponential at the start, moves towards an inflection point (which is the peak of daily infections), and then appears to exponentially approach the asymptotic limit of the maximum number of deaths.

My understanding of the Hubbert linearization is that new cases / total cases is an indicator of how far the epidemic is in its "lifetime" - that it goes down linearly from the outset to the conclusion of the epidemic, where it ends at zero.

So it's not clear to me how new cases / total cases could be used as a comparative measure across countries, when each country is at a different stage of its epidemic relative to the other countries.