I mean, who wants to feel like they work at a bullshit job where nothing matters? If you can sell putting on a show of dramatic urgency at any level you'll find lots of buyers (at least until the disillusionment sets in)
(I do wish Spock had been a Bayesian and said something like "the probability of us surviving is β(17,82)" since you kinda need error bars for your probability estimates if you are putting them to work.)
The first or second crews to have been wiped out (even if their chances of survival were higher) would have made for a much shorter story.