To be more specific, vaccination does help reduce transmission, partially, for a short period of time, but it's reduction in transmission is low compared to it's significant reduction in severity.
To be clear, it's totally fine that the vaccine doesn't really do much for transmission. That's not the goal. Covid is certainly here to stay and it's probably going to be a seasonal illness much like the flu - and we might even see seasonal covid shots like we do with the flu. We only care that the severity and hospitalizations are kept low. The vaccines do accomplish that and with basically no side effects.
I don't think I disagree on the other points. I'm fairly certain you're right about seasonal COVID shots coming, and there's no doubt about the vaccine's importance in ameliorating symptoms. Communicating all this will be interesting. Something that's always been communicated poorly about influenza vaccines, for example, is that people who got a bad case of a strain they were immunized against would quite possibly have been a lot worse off without the vaccine. (Pet peeve: influenza A can be quite dangerous and that's not communicated well.)
https://www.forbes.com/sites/roberthart/2021/07/23/pfizer-sh...
Since this is something people commonly write around here, I am truly curious to know what you read that lead you to believe this? It's weird how many people believe the vaccine is not effective in stopping transmission. It's not 100% effective, and how well it's working to prevent transmission is a moving target as the virus changes, but if you think the effectiveness number is zero percent, I would like to understand where you got that. I'm pretty sure the official numbers are still above ninety percent, even with Omicron.
(it is of course true as you hinted that the vaccinated have less severe cases and shed less virus, etc.)