...though just as much evolution occurs during replication in unvaxxed people

That's not quite my understanding. The key point is that vaxxed tend to encourage the survival of mutants with different spike proteins. Those mutants have, after all, a better chance of evading the imperfect immune response produced by the vaccines. There is no such advantage in the unvaxxed. There is an evolutionary pressure in anything but full sterilizing immunity.

The evolutionary mechanism seems much the same to me as what drives the development of antibiotic resistance.
(Apologies to Geert Van den Bossche if I've butchered anything too badly in this layperson's summary.)

*Ochre Harebrained Curmudgeon*