Your comments above make sense, and hopefully the idea of a vaccine passport will simply be a transitional solution to some normalcy until we (hopefully) get to a point when Covid is not a serious threat any more. Think of the current pre-testing requirements as the first phase of that "transition" (allowing people to travel if testing negative) and the vaccine documentation as phase two (adding vaccination as a valid travel authorization). Phase three would be enough vaccination that the real threat is no longer acute, so vaccine documentation becomes superfluous, as you note, and we could go back to the way things were prior to March 2020.
I think the key question is what is the ceiling for vaccination? Can we get to 85% to 90% vaccinated, a level that would likely make "vaccine passports" irrelevant? Or, due to vaccine hesitancy and the politicization of vaccines, will we struggle to get above 70% coverage? If 30% remain unwilling to get the vaccine, we may have to prove vaccination for a long time. If we can convince the hesitant part of the population to get vaccinated, and can get the U.S. to 85% to 90%, then I think domestic U.S. vaccine passports will indeed become irrelevant as you suggest. Given the time it will take globally to reach very high vaccination rates and the difficulty of vaccinating the poorer, developing nations, I suspect some sort of vaccination proof may be required for international travel for a long time.