Perhaps it’s simply because a tragic background and the resulting emotional scars are an easy way to explain the characters’ motivations?
Assume for the moment that the Waynes had not been murdered when Bruce was young. Where does that leave him? He’s absurdly wealthy, good-looking, and (even without the tragedy-driven obsessive streak) possessed of incredible physical and mental talent. Without some sort of traumatic, unbalancing experience, what would have driven a man with his advantages to risk his life chasing criminals every night? He might have been a pro athlete, or a brilliant scientist, or just been the rich playboy he often pretends to be…but he wouldn’t have been Batman, and we wouldn’t have been reading about him for decades.
There are other motivations, to be sure. A superhero could be essentially a mercenary, hired to fight crime by the government or a wealthy individual with an axe to grind. He could be driven by altruistic impulses. He could want to test the limits of his gifts, and chooses to target criminals simply because they’re more of a challenge, or because it doesn’t get him into as much legal trouble. He might just want to be famous, or admired.
Variations on many of these themes have been used, but none seem to have had the resounding success of the angsty types. The typical audience for the superhero genre must like the tragic figures for some reason. Maybe it’s because it’s inspiring to see someone rise above his pain to achieve great things. Maybe it’s because the other motivations are harder for the target audience to empathize with–vengeance is easier to understand than altruism for most people. Maybe it’s just habit, at this point.
Regardless, the writers (who are typically under pressure to come up with material fast) often take the path of least resistance. The tragic background is a crutch, well-worn but reliable, and it’s not hard to see why they keep falling back on it. After all, it sells.