As far as we know, no country is approaching saturation yet - e.g. if 10% of population has been infected, then that would slow the infection speed just by 10%

As far as we know, no country is approaching saturation yet - e.g. if 10% of population has been infected, then that would slow the infection speed just by 10% which would not be noticeable in these scales. The total population will become obviously relevant if, say, 30% or 50% of the country is infected, but that's kind of the worst case scenario that we'd like to avoid.