Furthermore, I'd imagine that ethically, we can't run a real controlled test. You can't put 1 infected, coughing person in a room with 100 other people. 50 vaccinated, 50 not. And see who does and doesn't catch it and/or die.
It would be manslaughter or reckless endangerment or something.....
So, the aggregate numbers are going to always suffer from behavior. Do vaccinated people take more or less precautions than unvaccinated? It depends, but I bet on the average many vaccinated still are keeping relative distance from others and still using a mask, depending on the situation.