I forgot about all the internet epidemiologists. I guess I'm guilty.

Every new infection increases the chance of a mutation.

But vaccines DID, certainly initially, reduce the number of infections. They also made the resulting infections less severe, so they lasted shorter amounts of time, resulting in less chance for mutations. The named  mutations I'm aware of came from Covid "long haulers."

And it's not a coincidence that the worst case rates, and the worst death rates in MO, after vaccines were available, were very much in the least vaccinated areas of the State. Kind of like measles are resurfacing now in populations with low vaccination rates.