The COVID vaccine was designed to reduce the spread of an infectious disease, seems to fit the definition. Is there a different vaccine you refer to?
If it made society better by "preventing infectious disease" that was a side-effect.
That one doesn't do that though.
In fact, some forms of the polio vaccine can give you polio. https://www.cdc.gov/vaccines/vpd/polio/hcp/vaccine-derived-p...