Per your point, when it comes to epidemiology, it does not make sense to talk in absolute terms (i.e. vaxxed people do or do not spread the virus). It is a matter of probabilities. Vaxxed people can get breakthrough cases, particularly with omicron, and they can be asymptomatic spreaders. However, your odds of contracting covid are much lower if you are vaxxed; your odds of significant, life threatening or debilitating long haul systems are much lower if you are vaxxed; and your odds of being an asymptomatic spreader are much lower if you are vaxxed; and as you note, vaxxed people, if they are in the small fraction of those spreading, carry a much lower viral load than the non-vaxxed. But in the days of omicron, masking and socially distancing are still excellent practices even if someone is fully vaxxed.
I was in France last month, right when omicron was hitting, To go anywhere (ride a train, eat in a cafe, go to an indoor entertainment event), you have to show proof of vax status or a negative covid test in the last 48 hours (all the pharmacies do walk-in tests). No French person i knew saw these precautions as a slippery slope to totalitarianism. They appreciated the piece of mind it brought (call it freedom from anxiety).
Also, youcancallmeAl, vaccine passports are not unprecedented in US history; a version of the vax passport was key to eradicating small pox:
History of vaccine passports in the US
Plus, public schools require proof of vaccination (or a religious exemption).