I'm not familiar with the elimination of smallpox, however, it is fact that the criteria for a polio diagnosis became much more stringent the same year the polio vax was introduced... sort of the inverse of the oft cited reason for increased autism diagnosis more recently.
In addition, textbooks also recognize sanitation and better understanding of polio as reasons for decline that are independent of the vaccine (makes sense since polio is transmitted oral fecal route). Don't get me wrong, I'm sure the vax has helped (I would assume), although i think it is very clear that the idea that vaccination eliminated polio is not supported by facts. Also, you may be interested to hear about "provocative polio" which has shown that needle pokes leave people vulnerable to polio for some reason.
"
The application of epidemiological surveillance and statistical methods enabled researchers to trace the steady rise in polio incidence along with the expansion of immunisation programmes for diphtheria, pertussis, and tetanus... The impressive volume of literature on polio provocation by the 1950s fuelled changes in health policy. US health organisations and charities, including the National Foundation for Infantile Paralysis, the American Academy of Pediatrics, and the American Public Health Association, accommodated the possibility of polio provocation and encouraged health professionals to avoid “indiscriminate” injections and “booster shots” during epidemics."
https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(14)61251-4/fulltext