All of the stuff I've read and heard from generally reliable sources (such as WHO officials, professors of epidemiology, etc) seems to suggest that Covid-19 will never be eradicated and it's not even the intention to try to eradicate it.
The aim is simply to bring it down to the same level as seasonal flu, where those most at risk receive regular vaccinations but, even so, several thousand people will still die from it (or from complications caused by it) every year in this country. [Last winter about 15,000 people died from flu infections in the UK].
So it seems that Covid-19 will most definitely NOT go away altogether.