Eradication of the virus is not going to happen. What most likely happens is at some point the virus adapts to humans more and will become endemic like other coronaviruses. It will then generally produce mild symptoms in most people and wont need a vaccine for it. I.e. it WILL become "another cold". This could take many years. The 1890 pandemic which has been postulated as being caused by coronavirus in a couple of papers, had waves over 4-5 years. By the way, the mortality pattern of that event closely resembled Covid.
https://pubmed.ncbi.nlm.nih.gov/29336941/
"Age-specific excess mortality rates displayed a J-shape pattern, with school children aged 5-14 years experiencing the lowest respiratory excess death rates (8.8 excess respiratory deaths per 10,000), whereas older populations aged greater than or equal to 70 years had the highest rates (367.9 per 10,000)"