Either way, vaccinated and unvaccinated people are catching and spreading the virus to vaccinated and unvaccinated people. If this is about controlling spread, then the argument for vaccine passports is nullified.
Ok, first, the article you linked to doesn’t support your statement that the CDC doesn’t agree with the statement that vaccination reduces the likelihood of transmission.
But I also don’t agree with the conclusion you’ve drawn from the fact that both vaccinated and unvaccinated people are able to spread the virus if infected. Your argument only stands if both groups are both infected and transmit onwards at identical rates. However that certainly isn’t the case for the first, and it’s an uncertain picture for the second. But with the first alone, even with delta, the risk is more than halved.
If we’re looking to control the spread, the obvious thing to do is have measures to reduce the R0. It’s well established that in a vaccinated group, even if some have the virus, many fewer will be infected as a result, and will therefore not create onward chains of transmission.
That’s without considering whether those who are vaccinated but infected are a lower risk overall, as the Singapore study quoted in the Nature article you linked to suggested based on clearance rates, and as Imperial have suggested for asymptomatic infection.
In fact, if your goal was to control transmission at a certain level, vaccine passports are going to be something to consider.
If you’re looking to eliminate transmission, I agree it’s fairly useless. But if you’re looking to create fewer onward chains of transmission at higher risk events and venues, limiting it to a population with an effective R0 of 3 rather than 7 is quite a logical approach.