1. Likelihood of breakthrough infections.
2. Mutation rate.
3. Initial volume of infections.
For instance, if the likelihood of breakthrough infections is low enough to overcome the reproduction rate, the mutation rate is slow enough, and the initial volume of infections low enough, you'd expect that the virus would die out if enough people have had the vaccine, right?
On the other hand, if the likelihood of breakthrough infections were high, mutation rate were high, initial volume of infections high, makes sense that you would expect to see ongoing mutation.
Another way I think this might go is that mutations happen & breakthrough infections happen, but the breakthrough infections further boost immunity, and the severity never re-approaches the original severity of covid.
https://www.washingtonpost.com/health/2021/03/11/immunocompr...
Considering cross-immunization between variants with natural immunity, it might be more efficient to refrain from vaccines to give cross-immunity with a weaker variant.