Early on in the Covid pandemic response claims of herd immunity were being thrown around and Fauci was claiming a threshold of 60-65% vaccine rate for it to work. As time went on that number kept going up, eventually he admitted that they used a low number to start with only because they didn't think people would comply if the required vaccine rate seemed unrealistically high.
Herd immunity is almost certainly a thing at a certain immunity rate, the question that goes unanswered is what that rate actually is. For there to even be a case for vaccine mandates, of even just the arguments that people ought to get vaccinated due to herd immunity, we have to know the % of immunized population and the risk of vaccine side effects.
My understanding is that we don't have a solid understanding of the exact tipping point for herd immunity, and that at least during the covid pandemic response we didn't have a solid understanding of the true risks of adverse side effects to the vaccines either.
You've missed a significant strength of vaccines by focusing on individuals rather than on populations.
Vaccines slow the transmission rate through a population and reduce the severity of infection.
In a population with a high vaccination rates those few with weak immune systems have less exposure to infection.
It's similar to back burning and fuel reduction in combating wildfires.