Your first paragraph is correct, but you seem to think it's a problem that people might choose to be naturally infected. That's a valid choice people can make. I believe most people who aren't vaccinated are doing so on purpose. Delta has actually been helpful towards getting herd immunity because is it so contagious but far less lethal than the earlier strains.

We can reach herd immunity with a combination of vaccines and natural immunity. You will not be able to vaccinate everyone.