The fact of the matter is that the incidence of those terrible contagious diseases was already drastically decreasing before vaccinations were introduced, caused by better hygienic, nutritional and medical conditions. After (sometimes even forced) introduction of vaccination in some cities, the practice was soon abandoned as it became clear that vaccination only led to more deaths. Yes, I'm not kidding.
Your last part is spot on. A randomly placebo controlled double blind trial to prove the efficacy and safety of vaccines has never been carried out, so there isn't even proof that that assumption is correct.