Ya, this is pretty wild.
First, he's just straight up wrong that the vaccines do nothing against transmission. Even with Omicron 2 shots reduce it by around 30% and with a booster its more like 70%. Its not as strong as it was pre-Omicron, but he's simply wrong, nothing more to say there.
Regardless of vaccines though, people would not be doing what he wanted them to do even if we didn't have a vaccine. In fact, I don't think people would be even THAT much more careful in a world without the vaccine. Unless there was news that it was coming soon I might even argue that they would be less careful at this point. Some people are still willing to be somewhat careful and take precautions because they believe all these countermeasures will eventually get us out of this. If they didn't see that coming, they would not be. We're two years into this. That's an eternity in people's lives. You really can't force people into their homes for years on end. Would better testing, masks, in some cases better public health choices, help? Of course. But 2 years in people in all but the most repressive countries would always be pushing back against heavy handed control, because people feel a need to live their lives.
Even beyond that, even if you could somehow get the US to commit to this, it would fall apart as soon as you went back to normal if the rest of the world didn't do the same. Someone would inevitably bring it back in. Are you going to force every country in the world to do this hugely authoritarian thing? How is that remotely feasible? He isn't making sense. Very much reads like someone who has zero understanding of human nature.