See, Cliffy, I pretty much disagree entirely about Destruction. Especially in Brief Lives, we see how much he dislikes the fact that all he’s responsible for is destruction. In fact, once Dream and Delerium finally do find him, he mentions something about how he couldn’t leave behind his sigil and drop someone else into the same mess (paraphrase; I don’t have my books with me here, unfortunately). Destruction seems to be the only one of the Endless who really didn’t like his job. The eldest three seem to be chained to their duties (in Destiny’s case, literally) and they all have varying feelings about the trappings of said duties (Death seems to wear her lightest of all). The youngest three seem to find that it all amounts to little more than a game. Well, certainly Desire feels that way, and Despair just seems to follow her twin. Poor Delerium, well, no one can really tell what she’s thinking. Destruction, therefore, is caught in the middle. He understands how important their functions are, but he also does not wish to be responsible for the consequences of his function.
As the quotation provided above from Brief Lives indicates, he’s seen this before. Beings realize that light and matter are not incontrovertable and soon (soon is relative when talking about the Endless) nuclear weapons follow, and then it’s a time of complete destruction. This is not something he likes to see, even though it’s essentially What He Does. All the Endless know that life is cyclical, and for this go 'round the cycle, Destruction decided he didn’t want to ride it out. It seems to me that his motivation was not, in fact, hedonistic at all, but more like a man who is giving up. If he left, his reasoning went, it might change the cycle. Or not. Either way, he wasn’t going to be in charge of it all anymore.
I also think it’s unfair to say that he didn’t care about the people that had been killed in his siblings’ quest to find him. He was unwilling to be found, and as such, put in place some safeguards to assure that he wouldn’t be found. The only reason his safety measures didn’t prevent Orpheus from telling his dad the location of his uncle was that Orpheus was family, and Destruction was unwilling to spill family blood. I mean, the Kindly Ones are no joke, y’know? Anyway, he didn’t want to be found. But I don’t think you can say that he didn’t care that people got hurt on the way to find him. In fact, I’m pretty sure that, had the seekers not been his family, his safety measures would have merely eliminated the questers, not everyone around them. Plus, y’know, he was in love with the dancing lady, so he’d have to be incredibly callous not to care that she died.
Anyway, in the end, you have to contrast Dream and Destruction. Destruction could have destroyed himself in the way Dream did, had he had the complete dedication to his duties that his older brother did. But Destruction had the gumption to just get up and leave while Dream, and this is what makes his story truly tragic, could not.