It doesn't need to be eradicated. If it mutates slower, vaccinations and herd immunity would mean the symptoms experienced are mild and your resistance would build on that as time goes by being exposed to new variants which are only slowly mutating.
> Many common cold viruses are coronaviruses, and we haven't eradicated them either.
There's hasn't been an incentive to - cost high, benefit low, after all it's just a cold.
Maybe that will change now.
There are new weapons in humanity's arsenal in the form of mRNA vaccines, and a huge incentive do develop this and to take these viruses more seriously.
