I think the ethical damage an act like that would cause psychologically makes even that semi-rational action a bad one to take. Thinking it in the abstract is different from having to spend weeks locked away in isolation underground pondering the neighbors or just human lives that your actions ended - even accepting the fact that you didn't initiate the ICBM and that if you didn't live where you did there'd be no bunker to possibly save people... I'm pretty sure everyone would be coming out of the bunker severely damaged with survivor's guilt and constantly second guess if maybe it would've been okay to let one or two in...

Basically, in the abstract, and in pop culture according to video games and movies... your approach is the way to "win", but the human psyche is a fragile thing.

(I'd clarify, this isn't meant as any sort of criticism, I just think that considering these sorts of scenarios in a abstract sterile setting is very different from how you'd experience them as they happened - and that's interesting to me.)