The year my brother and I was born, we apparently got a bad batch of MMR, meaning it wasn't foolproof. When we were teens, my brother and I both came down with the mumps. They were very mild. Zero other students got sick. Zero. Because, as you point out, you don't get mumps, measles, etc. vaccines and then expect to get sick. The bad batch of MMR still managed to kick coronavirus vaccine's butt.