What you are referring to is eradication, which has only ever been performed twice. SARS-2 is functionally impossible to eradicate due to its zoonotic origin and incredible spread.
Even with herd immunity SARS-2 is here to stay. That’s not a problem though, even if we could so something about it. Why? Because SARS-2 kills the very old but spares the very young. Therefore once it has passed through the current population, the set of SARS-CoV-2-naive individuals becomes dominated by new entrants to the world, meaning babies/toddlers, the same group that does not die to COVID-19 in any real numbers. Therefore unlike Influenza, recurring deaths from COVID-19 will be incredibly low in subsequent years.
Why would you willfully ignore the enormous research literature showing enduring immunity developing from SARS-1? Oh, right, because either you haven't read it or you don't like that it doesn't support your conclusions.
It's like, imagine we're discussing H1N1 reinfection, and we have a highly similar H1N0 which varies very slightly, and we know that doesn't lead to reinfection. But instead you look at a number of Influenza viruses in the same family but not nearly as similar.
Don't you see how ridiculous that is?
We obviously should use SARS-1 as a model for SARS-2.