If you only have 100M doses and you waste half on undetected positives, that definitely hinders achieving herd immunity. Unless you are saying uncontrolled spread helps develop herd immunity. It does, but it isn't a desirable method.
Nobody said it was a desirable method. But I did assert that past infections does reduce the doses you need to give to reach herd immunity, which is a point you seemed to argue with.
We'll likely be at >70M natural infections before vaccination efforts hit full steam in mid-January. This is pretty close to the lower end of where models predict herd immunity effects (not ~60% because of non-uniform contact graphs and susceptibility). You don't need a whole lot of vaccination tacked on top of this to start to tamp things down, even though A) some of the vaccinations will be wasted, and B) the vaccinations will not be as "on-target" to break important links in the graph as infection itself is.
Sorry for the misunderstanding. I wasn't arguing that past infections change the needed doses, I was arguing that undiagnosed positives waste limited doses. Hope that's clarified.