> more people developed immunity

Better yet, those who survived prior plagues were more likely to already be immune to the disease, and evolutionary pressure led to a more resilient population against this type of disease.

Potentially, but I am a bit sceptical. Plague reached a lot of new territory during the third pandemic (for example, australia and the americas), while still having a low mortality. One could check whether native populations to those continents were especially hard hit compared to people from European descent. I haven't heard anything like that.