FDA has a careful process for approving vaccines. I got to thinking the terms "safe" and "effective" are usually said in the same breath. My guess is that "safe" takes less time to test than "effective."
One can get data on the safety of a vaccine pretty quickly if people in the trial aren't having bad side effects.
As for testing effectiveness, people in the trial would need to be exposed to the virus to see if they have immunity. That takes longer as in the normal course of events, not that many people, in the sample, would be exposed. Exposing folks on purpose brings up ethical questions.
Maybe they could separate the two concepts of safe and effective?
If a vaccine is safe, at least in the short run, (not counting possibly some strange cancer 20 years from now), maybe they should distribute it farther and wider? If it's safe though not effective; little is lost.
I would guess it's especially not a big loss since quite a bit of the COVID-19 vaccine has been already manufactured, in this case, to jumpstart eventual distribution. Vaccine that is not safe and effective will have to be thrown out anyway.
A premature distribution could mean a larger pool of people for trials. This would make it easier to test for effectiveness as a larger group of people means more would come in contact with the virus at some point in their normal lives.
Just a thought. Maybe they are doing this, I wouldn't know.
There is also, of course, the worry about public trust of a vaccine when it does become available. I realize that is one reason for caution.