To be serious the doc from the game(I don’t know what the series did.) is simply not qualified to do such a surgery since he simply seems to be to young to be more than assistant doctor.

Even then isn’t it revealed that the doc cares for the animals of the zoo of salt lake at the beginning of Abbie’s flashback? That requires veterinarian knowledge he seems to have so he is even less

A weak argument is that a he should be able to take probe from Ellie(carry out a biopsy) without killing her.

Another argument if Joel did the moral thing is how would have the firefly’s used the vaccine if they could have created it? They seem to have done quite some bad things according to Abby’s dad so I wouldn’t trust them to have the best intentions with it.