It is not possible to eradicate SARS-CoV-2. We eradicated smallpox and (almost) polio because we had highly sterilizing vaccines and no animal hosts. That situation doesn't obtain with SARS-CoV-2. Vaccines are highly effective at preventing deaths and I do encourage vaccination, but vaccinated people can still catch and spread the virus. They are probably less contagious on average, but unfortunately that isn't enough to control community spread.

https://www.nature.com/articles/d41586-021-02187-1

https://www.nature.com/articles/s41586-021-03944-y

there is a too many unknowns for anyone to be able to say its not possible to eradicate covid. whats known for sure is that ~40% vaccination rates would have not been able to eradicate either smallpox or polio...