And there's the fact that Omicron mutated a whole lot without spreading (it doesn't share a lineage with Delta) which makes me think that this naive form of evolutionary pressure cannot be responsible for its reduced lethality.
That isn’t the only form of evolutionary pressure. The more your host population builds up immunity to the viral bag of tricks the more evolutionary trade offs there must be to remain infectious and over time they tend to harm the virulence. For example, Omicron seems to be very good at replicating in the upper respiratory but not so good in the lungs. Destructive mutations can still occur but they become much less probable over time.
> Omicron mutated a whole lot without spreading
One theory is that it did mutate through spread but in mice not humans. [1]
1: https://www.biorxiv.org/content/10.1101/2021.12.14.472632v1....
Are you sure about that? RdRps have quite the error rate, which means faster evolution. (And yes, I'm aware that the error rate in these vary based on the RdRp's sequence, but in either case, these are both higher than DNA transcription.)
I do agree with the rest of your comment. Go get vaxxed, people!
Not much we can do to stop that.