Vaccinated people can and are spreading Covid just the same as unvaccinated. That is a fact. So what is the benefit of allowing people into a room just because they have a pass to prove vaccination, and denying them entry if they do not?
It's all about encouragement for the greater good.
A different scenario. Why punish a person for driving a car without a licence? A 20 year old unlicensed person could very well drive a car and react quicker than a licensed 80 year old. If you had to suddenly step out in front of a car, who would you expect to stop or swerve round you - the 20 year old unlicensed driver or the licensed 80 year old? Again, it's for the general greater good to 'encourage' all those who want to drive a car to take a test.
We elect a government, they make some rules, we follow them or get punished. Been going on for years.