I didn't say the mutations happen in vaccinated people. I said vaccination placed evolutionary pressure for the virus to evolve. Again, it's basic biology. The original strains can't infect the vaccinated as easily, so only the viruses with mutations will be able to go around and they got a clear field (le champs libre).
The exact same thing you are describing would happen after enough hosts would have acquired natural immunity through infection...
Edit: and that's the advantage of vaccination acquired immunity. Yes you are right, sterilization immunity will get bypassed by evading mutants (both true for vaccination and infection immunity) but the vaccine provides a proven safe way to prime your immune system for a much milder illness course.
Data is already showing that vaccine or infection immunity grants a much milder illness when contracting omicron.