I don't even think it is a crucial element. If the choice is between sacrificing a child or let an ongoing plague torment humanity, it's right to sacrifice your child. Whether or not you'd be able to do it is a whole different story (and that story is named TLOU)
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The strength of the game is not making you think if what Joel does is right. It's making you understand there was no way he'd do anything else.
Not saying your interpretation is wrong btw, just not the takeaway I had (plus the game's creator thinks Joe's decision was admirable, so idk)
It felt quite clear in the emotional subtext of the latter section of TLOU that Ellie understood death was a strong possibility.
https://www.youtube.com/watch?v=1qKC-BiMTX0