Vaccine passport proponents routinely cite "slowing [the] spread" as a reason to impose vaccination requirements despite discoveries earlier this year showing that vaccinated individuals can still spread the disease. In light of these discoveries, vaccine passports and other coercive measures don't make any dense.
Delta has an R value of 8. That makes it one of the most infectious diseases we know about. Future variants are likely to be even more contagious. (That's the evolutionary pattern we see in other diseases.) Even if universal vaccination were to somewhat reduce the R value, the R value would remain above the critical threshold value of 1.0 regardless --- because R starts out so high naturally. We know R is above one post-vaccination because highly-vaccinated places like Iceland and Gibraltar see COVID waves despite near-universal vaccination. If R is above one, everyone will get the virus sooner or later anyway no matter what, and we are not operating in the regime in which universal vaccination has the kind of large positive externalities that might justify a universal vaccination program for other diseases (e.g. measles).
It's only large positive externalities that can justify state intervention in individual health. (The 1905 SCOTUS case that people have been citing discusses the issue in detail.) Current COVID vaccines, due to the R-value threshold effect, don't have the large positive externalities attached to previous vaccines.
As an analogy: a leather jacket might reduce a bullet's velocity to some extent, but that bullet will still penetrate and kill you. Nothing short of body armor that can actually stop the bullet is effective. Likewise, unless the vaccine can reduce R below 1 --- and no current COVID vaccine can do that --- universal vaccination cannot stop the spread of the disease.
The vaccines may be beneficial, but being beneficial, by itself, doesn't present a case for coercive state action. If it did, we'd probably all eat healthier and exercise more --- and we'd be less free as a people.
There are real social and economic costs to creating a "papers, please!" culture and setting a precedent for state intervention in individual medical choices. As it stands, the low risk posed by COVID and the insufficiency of current vaccines can't the coercive state programs being proposed around the world.