The fundamental problem with this question (and indeed, the premise of this entire thread) is that it's dealing with hypothetical scenarios that never existed. So it depends on what you model: what level of restrictions are you including in the alternative scenario, do you cut off vaccine access at 40, 50, 60, do you consider the increased possibility of mutations as the virus circulates...? The answer varies significantly, and I don't think there's a neutral ro objective answer to these considerations.
That doesn't make it a bad question, but I think it makes it fundamentally unaswerable from any objective position. You can make reasonable inferences and claims, but that's it. People both more or less for/against lockdowns and more or less for/against vaccinations would benefit from remembering that point and being cautious accordingly!
There was a pretty extensive observational study of the vaccinations and their impact on transmission of Alpha and Delta:
https://www.medrxiv.org/content/10.1101/2021.09.28.21264260v2, which concluded high level and waning-but persistent impact on transmission of Alpha, with low and more quickly waning impact on transmission of Delta.
I think it's pretty well established that vaccines have had a more limited impact on transmissbility of Omicron, but research is necessarily more tentative:
this suggests some but short-lasting impct but note it is not peer-reviewed yet (published August 22). But then there's other research which suggests that
prior infection makes you more prone to catching Omicron so in that sense vaccines may be preferable to infection dervied immunity. As different waves of Covid and vaccines circulate though it will become increasingly difficult to come to any meaningful conclusion as the number of possible vaccine-infection histories proliforate.
