I don't think so. For instance, coronaviruses are among the causes of common cold. That one seems to have been with us for a while.

OTOH, a large number of infected people means a large pool of viruses to mutate into potentially re-infective strains.

No, it means that the expectation that "herd immunity" will be naturally reached, without an effective vaccine, is a pipe dream. Before vaccines, no population ever reached "natural herd immunity" for polio, which has similar R values; you need effective vaccines, effectively delivered, to get that result.