there's something about batman that's qualitatively different from other super heroes, and thus people's fascination with batman.
first, batman is more down-to-earth. He can't fly. Doesn't have magical powers. He can, conceivably be the guy in your neighborhood. And he's rich, of course, and there are lots rich people around. Batman we can associate.
He doesn't have the typical pro-American shit as do Superman, Wonder Woman, Captain America, putting flag all over their body, by American for American ass. And that despicable spider-man with his “great power comes with great responsibility” White man mentality and wimpy cowardly indecisiveness. (this is called Slave morality by Friedrich Nietzsche)
batman is a psycho. A quality we are fascinated with, and actually a mental “illness” that afflict some 1% of people. The whole shebang of batman universe is a play on psychology. Joker, Penguin, 2-face, …, and of course the romantic cat-woman, who can't tell the difference between love ＆ hate.