That makes no sense.Companies had to prove that the vaccine was...

That makes no sense.

Companies had to prove that the vaccine was safe and that it reduced people getting ill.

That being the case, if you are less ill ie less likely to cough or not coughing at all, naturally this would mean that you are less likely to transmit the virus or have reduced your transmissibility of it.

It doesnt need to be proven..... If the former is satisfied the latter is also satisfied.

The logic is flawed. If we use it on another example say seatbelts in cars:

You only test them to ensure they dont hurt people using them and that they prevent you from falling out of the car in a car accident. But you never actually studied if they save lives.

As I said, many studies across the globe followed vaccination and showed reduced transmission. So are you saying that all these independent researchers are fake newsing or making unfactual claims?

Your talking about a rapid rollout during a pandemic. Do you honestly think that they will test for everything or just whats important?
Even if hypothetically it doesnt reduce transmission, if it makes you less sick from the virus is it better to have or just go without?????