This Story is based off not just the characters from the show but also my in vision of Daryl and his personality if the apocalypse where to actually happen and if TWD never existed.
So the prospect of not being here at some future date is simply not a matter of concern for him; there is nothing he could do about it anyway. It is just how it is, just as what now is is what is. Just part of the ever-changing nature of reality. He will do anything to do what must be done in order to escape the pain, and so evil vs. good it is. *cue evil laugh*