I’m not sure what you’re getting at. Are you saying that we should be “pushing for herd immunity through both means” as in we should be pushing for vaccinations and pushing people to spread the disease as fast as possible?
I'm simply stating the claim that US is pushing for herd immunity through the choice of infection of vaccination is not true. That only vaccination is being pushed, and it is not exactly a free choice if you're going to lose your job or be denied service over it.