Actually in some versions he does...
Key words, "in some versions." But some versions make less sense than others. It's frankly ludicrous to claim that someone who's clinically delusional could be a functional crimefighter at all, let alone the World's Greatest Detective. Knowing what's real and what isn't is pretty much essential to being a detective. So anyone who writes Batman as insane is not thinking it through.
Moreover, in the most recent version he broke a young girl's noise simply because she was following him around and refused to summon a doctor to help someone who had acid splashed in their face because "it is a family matter" - signs of a dangerously unbalanced individual with warped judgement.
Sounds more like badly out-of-character writing to me. Even so, what you're describing there is a personality disorder or just general jerkiness, not insanity by any clinical or legal definition.
The problem is, too many Batman writers are trying to do The Dark Knight Returns
, but TDKR was never intended to be a typical portrayal of Batman; it was meant to be an extreme alternate future, and in some ways a deconstruction and dark reflection of the lighter version of the character and his world that had prevailed in comics to that point. So some writers just make Batman gratuitously dark and harsh and brutal because they think it's cool. But that just doesn't fit a character who's voluntarily given up the cushy, comfortable life he could easily have because he's passionately devoted to making sure other people don't have to lose loved ones to crime the way he did. He's not about the kind of gratuitous brutality or cruelty you describe. He's about fighting those things, about stopping the kind of people who would cause unnecessary pain to the innocent. So I'd say the warped judgment there is the writer's.