Vaccination reduces the infection rate. [0] You can't transmit the virus if you aren't infected in the first place. Other studies have shown that people with breakthrough infections have a shorter period in which they can transmit.
[0] BNT162b2 mRNA Covid-19 Vaccine in a Nationwide Mass Vaccination Setting https://www.nejm.org/doi/full/10.1056/nejmoa2101765
This is another misconception. Our best evidence is that they're extremely effective. The problem is they're not quite effective enough to just go back to life as before since newer variants are extremely virulent.
Vaccines absolutely do reduce transmission from the vaccinated outward.
https://www.google.com/amp/s/www.newscientist.com/article/22...
https://www.newscientist.com/article/2294250-how-much-less-l...
Even given the typical bias of the media it’s still astonishing that Biden got a complete and utter free pass from the media for propagating this idea by basically giving everyone - vaccinated or not - a “mandate” that they no longer needed to wear a mask this past spring / late summer, all for PR points to make it look like the virus had been defeated.
The unvaccinated are banned as means to put social and financial pressure on individuals to get the vaccine. It is an unfortunate misconception that any of the currently-approved intramuscular vaccines reduce transmission to a meaningful degree.
This social and financial pressure is placed on individuals because urban hospitals do not have the money or resources to deal with the rate at which they're admitting patients for severe Covid-19, and most of the patients they're admitting are unvaccinated.