Childhood diseases like measles and polio were already disappearing due to better sanitation and nutrition; vaccines get undeserved credit.
This argument conflates mortality decline with incidence decline and misunderstands pre-vaccine history. While improved sanitation, nutrition, and living conditions did reduce mortality rates from many diseases in developed nations, infection rates remained catastrophically high until vaccines appeared. Measles, for instance, infected virtually every child by age 20 in pre-vaccine America, millions per year, causing thousands of deaths and permanent disabilities. After the measles vaccine was introduced in 1963, incidence dropped 95% within 10 years and has remained near zero in vaccinated populations. Polio exemplifies this perfectly: in 1952, the US had 58,000 polio cases and over 3,000 deaths despite excellent sanitation and nutrition. The Salk vaccine appeared in 1955; by 1960, US cases had dropped to 2,000, and by 1970 to near zero. Globally, polio incidence has fallen from an estimated 350,000 cases per year in 1988 to fewer than 1,000 today, this is entirely attributable to vaccination. Sanitation didn't eliminate polio in Pakistan or Afghanistan; vaccines did. The counterfactual is clear from contemporary data: in populations that reject vaccines, disease rates skyrocket within a generation, regardless of sanitation.