Sorry, that is not how mutations work, it's not a conscious act.
With more vaccinated people, the virus will have less places to live, and there will be less virus.
Every time a virus replicates, it has the possibility to mutate, so the larger the pool of non-vaccinated people so there can be larger amounts of virus will mean more mutations.
It's purely a numbers game as mutations which happen all the time are random and most are not effective.
You are correct there will be more mutations, as there have already been 100's identified, but only the significant effective ones get famous.
I understand the virus-mutation factory point about unvaccinated people, but all organisms adapt to overcome adversity -- or rather, to your point, things that work in a new environment expand while other things die out.
Potentially beneficial mutations are often present in a population but don't tend to advance due a lack of material advantage. But once the environment changes, latent advantages come to the surface and preference for those advantages accelerates.
Said differently, rabbit runs as fast as they do because they don't have to run faster. Send out faster foxes and you will get faster rabbits because the ones that are already marginally faster than average get to reproduce while the others become fox-chow. But right now, faster rabbit genes don't convey a material advantage, so they languish.
The vaccine evading variants don't have an advantage in most of the world right now. There is no need for the Covid-rabbit to run faster around the Vaccine-Fox...so vaccine-evading genes languish while sheer transmissability in unvaccinated populations (delta) takes off.
But vaccine-evading mutations will now convey a material advantage in Israel, England, the US and other growing parts of the world.
The Vaccine-Fox is picking up speed.
The faster Covid-Rabbit will not be far behind.
The beta variant (which may evade the vaccine) is now on the rise in France. Enough so that the British government just freaked out and went backwards on travel rules to France...except for commerce...which is covid ground hog day all over again. This will be ineffective just as it was ineffective against delta. The new variant will get into the system (I would bet anything its already here) and if it really can elude the vaccine, it will spread quickly.
The good news is that the world's drug companies are hard at work on faster foxes. This cycle will likely continue for a very, very long time.
My $0.02.