I do not agree on any single one of your numbered points.
1) "eradication is not possible" just does not follow from "this is a highly transmissible respiratory virus". "Eradication will be difficult" follows; but several countries have shown us that "eradication is entirely possible if proper measures are taken"
2) The purpose of lockdowns is to eradicate the virus. https://medium.com/@joschabach/flattening-the-curve-is-a-dea...
3) See 1.
So my position is that eradication is possible, and - given the possibility of multiple waves if the virus becomes endemic (large virus population --> increased chances of dangerous mutations) - it is vital that we give it a really good try.
The discussion should re-focus on how we go about eradicating the virus, while minimizing the damage to the economy. This article outlines an appropriate path forward: https://medium.com/@tomaspueyo/coronavirus-the-hammer-and-th...