>if P(death|vaccine) < P(death|covid) then it seems really barbaric not to give it.

No, it would have to be P(death|vaccine) < P(death|covid) * P(covid) because not everyone would get covid during the pre-approval period. That's a far higher bar.

Also, let's not forget P(covid|vaccine). People would behave very differently once they had the vaccine and feel safe. So if the vaccine isn't effective, that could be catastrophic.