Word was that Omicron diverged from an earlier version of covid in mice, over the course of about a year, then jumped into humans [0].
I think this detracts quite a bit from the point you were trying to make above, since we are not vaccinating mice, nor all the other animals that harbor covid such as bats, cats, dogs, primates, and deer [1].
Since we can't vaccinate or destroy all of the non-human hosts for this coronavirus, and the virus already has evolved in animals and made the jump to humans a couple of times, I don't agree that the point you made above is relevant.
[0] https://www.medicalnewstoday.com/articles/covid-19-did-omicr...
[1] https://www.cdc.gov/coronavirus/2019-ncov/daily-life-coping/...