My, also not epidemiologist estimate, would be that the only way to have any measure on the spread today when comparing countries is the number of deaths per capita compared to the strain of the healthcare system. Add some factor for the mean time from infection to death and you have it.

Everyone who is ill enough to be about to die will end up in a hospital, with the virus already being transmitted in the society the point in testing everyone else is trending towards negligible.

Sure if the measures taken allows the rate becomes low enough again, then contact tracing might become worth doing again.

You can also try to do statistical tests on some cohorts of population and extrapolate from there but if the resources are limited then saving lives counts more.