Walking through the math on partial immunity doesn’t change it much.
You can break the population into groups to get an estimate of average immunity. K percent are under 12, L percent have both vaccine and natural immunity from a previous infection, M percent have Moderna, N percent have J&J, P percent have pfizer, Q are uninfected anti-vax, R are anti-vax but previously infected, and so on.
Three of those groups are in the 95% immunity range. (pfizer, moderna, and J&J+natural) Two are 70-90% (J&J only, and natural only) And only two are below 70%. ( under 12, and anti-vax but never infected)
Add them all up, and you’re still well over the 67% herd immunity threshold for R=3.
Of course, if you have something like Eeek that changes the spike protein, your effective immunity of all kinds drops. You end up well under the herd immunity threshold, and you are back to needing NPI of some kind. Nor can you let it bloom and trust in a lower ifr. The lower ifr is based on vaccinating the elderly. To the extent a new strain ignores the vaccine, it also ignores the lower ifr.