It would be more accurate to say that Batman is more dedicated to stopping murderous vigilantes, than murderous supervillains.
Batman is afraid he would snap if he killed someone. He might feel, that if he didn't stop someone, who he actually wouldn't mind dying, from getting murdered, that he is also responsible, because he might have held back subconsciously, to let someone else do his dirty work. So he gives his 110% into stopping it.
And yeah, it varies depending on the work, but most of the time it's basically canon that he is almost as damaged as his rogues gallery in many ways, he has just found a more moral and constructive way to channel it. But yeah, no realistic police force would hire Bruce, after taking one look at his psych profile.
I've seen this line of thought before, and can even buy into it to some degree, but that only decreases my opinion of the Batman character further. Like, you
could claim that he only captures criminals and doesn't make judgements as to their punishment, leaving it up to the courts and therefore they are to blame for the revolving-prison problem.
...exceeept, Batman already picks and chooses what laws he's going to obey; just because he follows some of them doesn't mean he isn't imposing his own view of justice on people. Then there's the fact that as a vigilante himself often people can only judge by his actions - which can include attacking seemingly upstanding members of the public and government, delivering breakout serial killers to jail unharmed, and fist-fighting Superman if he so much as thinks about fighting crime in Gotham.
Gee, Bruce, I wonder what the citizens who live in fear of the Bat would think he wants, huh? I fucking wonder.
*Judge reading out list of crimes at the Joker's trial*
"...and thirty-
eight counts of first-degree murder... since your last trial."
"Thirty-nine.
honk!"
*Joker blows his nose with his dead lawyers tie*
"Again?"
*looks around* "Am I the only one that sees this?"
*sigh* "Mr Napier, I am not entirely sure how it is you have not found yourself having a little
'accident' on one of your many, many trips to our institution, but I feel I have no choice but to sentence you to Death Row, whereupon you will be sent straight to he-"
*BOOM!*
*Superman and Batman come tumbling through one side of the courtroom*
"I just want to help!"
"Stay out of this, Superman! This is
my city!"
*fzzeww!*
*Superman and Batman go tumbling through the other side of the courtroom*
"-uh, the nearest psychiatric institution, or, I don't fucking know,
daycare. Screw it, I retire."
*Judge storms away*
*Joker looks up from sawing through prosecution's neck with a batarang*
"Bye, yer honour!"
"Judge out!"
*gavel drop*
