This is false because COVID also has animal reservoirs. It will never get eradicated like polio or smallpox, which only had human reservoirs.
It appears that in 2022 it is now finally understood that COVID-19 will not get eradicated, the vaccines do not prevent transmission or infection (in fact, the original RCT never even showed it -- it was just assumed!), and that cloth masks have much more limited effectiveness than initially assumed. Omicron is highly contagious (but much milder!) so it appears that almost everyone will get it eventually.