Smallpox has exactly one host (us), had an amazingly effective vaccine, the virus doesn’t mutate quickly or spread as readily, and it still took almost 200 years to eradicate it.
Polio is NOT eradicated, it spreads only through contact with fecal matter, and the remaining areas where it is endemic make a great illustration of exactly why this virus isn’t going anywhere either: Afghanistan and Pakistan.
That you would suggest that either of these make an argument for eradication of a flu-like illness with multiple non-human hosts shows how detached from reality you have become.