The thing is, if the virus evolves to spread better amoung vaccinated people, and the large majority of the members of a population have immunity from vaccination or infection, as is the case in South Africa, there is no evolutionary pressure that the virus becomes less lethal for unvaccinated and immunologically naive people.

It could as well become more lethal for them, or certain new age groups within the unvaccinated group, without that hindering spread among the other parts of the population.