Trying to be a bird
Also consider Death: the Time of Your Life.The difference is, at least from what I've taken of Morpheus' discussions about the family duty with Death, Destiny, Desire, and most importantly Destruction, is that the event will happen without the Endless being present. But if the Endless chooses to take on the duty, then they are to blame for what the duty entails. Like, Dream creates nightmares and some of them will inspire serial killers or themselves get loose to kill people. That is horrible, but part of Dream's role. He accepts the responsibility for those actions, even if he doesn't have to be present for the nightmare to exist.
So Destruction walked away from the duty, in the belief that means all the destruction in the universe will no longer be his fault. Because when he was part of it, it was his fault. Now, I believe Destruction was fooling himself--engaging in the type of self-deception that Morpheus often did--but at least he didn't feel as guilty. Whereas I think Death, as the most emotionally mature member of the family, accepted that the deaths happened because she separates life from death. It's not "good" or "bad," and she has very limited control over who dies when, but then again, she's the one doing the duty. She just doesn't feel guilty about it.
She allows a deal, and not because of any kind of balance, but because part of keeping a foot in the human world is doing things for sentimental human reasons. And, well, she DID make a deal.