Law of large numbers. The widespread plagues of the past were never 100% lethal, or we wouldn't be here - a sizable fraction of the population survived, and over several rounds of infection/reinfection gained something we'd think of sterilising immunity.

In the meanwhile, the plagues and their knock-on effects may have eliminated approximately HALF of the entire population of their times.[0]

0: https://en.wikipedia.org/wiki/Black_Death ("is estimated to have killed 30 percent to 60 percent of the European population")

By letting people die. If covid came around in the 1200s, then everyone would have gotten it and ~3% of the world population would have died. Definitely suboptimal but nowhere near an extinction event.

Well, a lot of people died, mostly.