The first priority is to save lives and control the epidemic. To consider the possibility of eliminating or eradicating COVID-19, several factors apply, including how long the vaccine’s protection lasts and how effective vaccine programmes will be in achieving high coverage, among other factors.
Even the existence of a highly effective vaccine is no guarantee that we will be able to eliminate or eradicate the virus. One likely scenario in the context of an effective global vaccination programme is that the virus would become an endemic virus with a low level of threat.
In any case, vaccine manufacturers are ready to adapt their vaccines to the new variants. And importantly, the viruses only mutate if they can replicate, and for that they need to infect. Thus, preventing infection by all available means is the best we can do to protect ourselves but also to limit virus evolution.