If you correlate your statement to his statement,
Then the vaccination will stop after all of the people have already been vaccinated, cause the mutation of the virus will stop.
There is no need for this to be forever, the mutations only happen to someone who was "INFECTED" by the virus itself. it won't mutate if it doesn't have a host.
I don't think that this is realistic. Reaching a 100% vaccination is not going to happen because a few sceptics will always deny it. And the other reason is that your body not be immune forever, it looks like with corona we need to refresh the vaccine already after 12-18 months. For other type of vaccines this is usually 5-10 years.