I just read one of Pfizer's documents about their Phase III trial: It said they are going to enroll test subjects irrespective of them already having Covid-19. I think that might be a mistake unless they run T-cell activation tests on those people so they know if they had it or not.

It's perfectly valid to include those people in the trial, but randomly assigning them to the vaccine arm may not tell you anything (because they are already immune). Randomly assigning them to the control arm means it requires a longer trial to get enough people in that arm infected, which proves the vaccine works. If researchers know who they are, they can break that group out into two more arms, and show how the vaccine works for people who already had Covid-19.

Of course, how would they know if a test subject had Covid-19? Probably a lot of their subjects DID, but it was asymptomatic. So they would have to run T-cell activation tests on every candidate! I think their test might be quicker if they prescreened subjects and rejected those already immune.

Educating anyone benefits everyone.