If there is selective pressure preventing spread, mutation would seem inevitable. Covid has mutated many times already. The question is will the mutations this selects for make a flu that is worse or will does it wall off all possible mutations with 100% (or close to) certainty?
Mutations are inevitable no matter what. Many viruses mutate extremely quickly, probably because they are much simpler than a bacteria - that's why many vaccines stop working in a matter of months. While you're right about selective pressure giving preference to some strains, by limiting the spread of a virus you limit its potential to mutate since there are so many fewer viral particles around.
For example if 100 people get sick vs 10, the number of viral particles and mutations you can expect increases tenfold and the risk of one of those mutations being dangerous increases as well.
