IIUC, you want to vaccinate everyone to get actual herd immunity as quickly as possible so the virus can't spread before it has mutated into different strains.

The more of the population unvaccinated, the larger population available for new strains to generate in, the higher probability of multiple strains.

It's not guaranteed the current vaccines inoculate against new strains, so you could be right back at square one next winter, with a new virulent strain.