So I'd stop on the way up, on the grounds that a life could be saved without necessarily imperilling mine, and possibly not on the way down, on the grounds that an attempt to save a striken climber would most likely end up with two deaths, not one.
Irrational creatures, aren't we?
Maybe not that irrational at all - having saved a life might well be a much more rewarding experience than having got to the top of a mountain. If you said to me what would I rather achieve then it's a no brainer but Everest is a different environment and everyone goes into it knowing that. Your attitude would probably mean never actually getting to the top as you'd almost always encounter someone who at least appeared to be facing death if you didn't help. And based on that you are never likely to try and climb it. So the end result is that it doesn't attract people who can't pass someone needing help without helping them.