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.