Weren't these diseases already going away before vaccines?
Here is what the checked sources say. Each title links to the original.
Measles vaccines save millions of lives each year
Our World in Data says US measles deaths fell in the decades before the 1963 vaccine, probably thanks to better treatment of secondary infections, sanitation and nutrition. It explains that measles is airborne and so contagious that hygiene improvements like clean water did not stop its spread: nearly every child still caught it, about 3 to 4 million US cases a year, and case numbers only began to decline after vaccines arrived. Researchers estimate, using models, that measles vaccines saved 94 million lives worldwide over fifty years.
Contagious diseases in the United States from 1888 to the present
Researchers digitized US disease reports back to 1888. Cases of polio, measles, rubella, mumps, hepatitis A, diphtheria and pertussis fell after vaccine licensure. Comparing reported cases with a modeled estimate of cases without vaccines, they estimate 103 million cases were prevented since 1924 (range 72 to 148 million). That model assumes the whole drop after licensure came from vaccination. The authors note some diseases had shifting trends before vaccines; hepatitis A fell in the late 1970s, presumably from better water and sanitation.
Historical comparisons of morbidity and mortality for vaccine-preventable diseases in the United States
This study compared US cases and deaths before vaccines with recent figures (cases from 2006, deaths from 2004) for 13 diseases. Cases of diphtheria, mumps, pertussis and tetanus fell more than 92% and deaths 99% or more. By then endemic spread of polio, measles and rubella had been eliminated in the US, and smallpox eradicated worldwide. For most diseases targeted since 1980 (including Hib, hepatitis A, acute hepatitis B and chickenpox), declines were 80% or more; invasive pneumococcal disease cases fell 34%. The comparisons were not adjusted for other factors.