>>150080843 (OP)
Because he's versatile. His origins, aesthetics and "powers" allow him to be inserted into literally any kind of genre and story. You can put him in any period, any place, literally anything and anywhere, and he just works. You can make a silent screwball comedy set in France with Batman. You can make a completely straight supernatural horror with Batman. You can make him an Ancient Greek or some Egyptian Prince and it works. You can put him in the far future and it works. You can make him Iron Man or Sherlock Holmes with a bat on top and it works.
Batman works on a level very few other characters work. Superman doesn't. Spider-Man kinda does, but not really. Iron Man so-so, only if you tie him to the concept of tech. But even then, even if you can find ways to shoehorn other characters in other genres, it's not natural. You can write one or two horror stories with Spider-Man. You can put Iron Man in a Fantasy setting. But they're one-offs. Experiments for people who already know who those characters are. You can't say
>I'm making a whole new AU where Batman's a wacky Silver Age mentalist with low-tier telepathy and he travels through time solving Scooby Doo mysteries
With Batman it works. With Superman it doesn't. Batman just has the perfect equilibrium to allow him to be inserted into literally anything. Seriously, think of any story, and you can put Batman in it, whereas with 99% of other characters it's just not possible.