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I don't think it goes far enough. Men with phyisical disabilities should also be allowed to go with the women and children. Men in general are stronger than women so are more able to help themselves. When there is an emergency there is no time to sort out who has children and so forth.
The rationale behind "women first" is simple species-level maths. One man can father hundreds or even thousands of children in his lifetime. A woman has a limited reproductive capacity and a limited reproductive window. Ensuring the survival of women above all else gives the highest chance of reproductive success.
Now, we might question this from a standpoint of immediacy: “if the male in question has no offspring, then his greatest chance of reproductive success is to ensure that he survives to reproduce!” This has some validity, but it misses the larger social picture.
If we agree as a society to the idea of “women and children first,” then we are in essence agreeing that all men will defend both the species’ reproductive capacity (the women) as well of the offspring of all members of the species.
Thus, were we to have children, we could remain reasonably certain that in times of crisis, these children would be looked after by any other men they encountered. In turn, we agree to place the wellbeing of other people’s children above our own wellbeing. Such is the social bargain inherent in “women and children first.”
Now, if enough people refuse to participate in this particular social accord, the entire thing disintegrates. There will always be corner cases who will never comply with such an ideal, but a concerted effort to propagandise this particular social accord would see the main body of the bell curve adhere to it.
The larger question is, in the face of both our increased technological sophistication and the booming human population, does species-level social mathematics still make sense? There is a certain level of comfort in believing that the tribe will continue to care for your progeny should you expire, but perhaps it is no longer relevant; sufficient genetic diversity exists within the species at this point that in continuation of any one particular genetic line is functionally irrelevant.