The first two sentences of your article are
> Eradication is the reduction of an infectious disease's prevalence in the global host population to zero.[1]
> Two infectious diseases have successfully been eradicated: smallpox in humans and rinderpest in ruminants.
There is exactly one disease that has been eradicated in humans: smallpox, which took somewhere between 19 years and 27 years depending on when you consider the eradication effort to have started in earnest. We've gotten close with polio (after 40 years) and guinea worm (37 years). There are also a bunch of other diseases on that list where elimination efforts are in progress, but have not yet been completed.
Regardless, "eliminate COVID", should we decide to go down that path, is going to be a multi-decade project at best. It's also likely to be much harder than eradicating smallpox given the asymptomatic transmission and animal reservoirs. It might still be worth doing, in the same way that our eradication effort for measles is worth doing, but it's not worth holding up anything important until the effort completes considering that "until the effort completes" is likely to be a couple generations at the earliest.