A complicated example of your point about "priming the immune system to overreact" is https://en.wikipedia.org/wiki/Dengvaxia_controversy https://en.wikipedia.

A complicated example of your point about "priming the immune system to overreact" is https://en.wikipedia.org/wiki/Dengvaxia_controversy https://en.wikipedia.org/wiki/Dengvaxia_controversy Dengue fever is a strange and terrible disease where -- unlike most infectious diseases! -- contracting it once can make future infections worse through autoimmune mechanisms (if I remember correctly, you typically become immune to the particular strain that caused the first infection, but may become more susceptible to severe reactions from a later infection involving a different strain). Apparently the Dengvaxia vaccine, while effective at reducing the chance of dengue infections, also has an effect similar to surviving an infection: it increases the chance that an infection will result in severe disease. That makes it a more complicated question whether it's a good health intervention in particular circumstances, and in the Philippines there was a big scandal where a childhood immunization program using it may have reduced the total number of people who contracted dengue, but also increased the severity of the worst cases. To my knowledge the pathogens that cause COVID-19 and dengue fever are extremely different, but it seems logically possible that there could be a COVID vaccine that greatly reduced people's chance of getting sick at all, while also increasing the chances of severe symptoms for those people who did get sick.