While I'm exactly in OP's boat in my appreciation of the character and the movies, I don't believe there's a hard rule about what exactly a faithful depiction of the character is or should be.
It's such a pop icon that honestly, the character is whoever people imagine he is, there's no right or wrong answer there. People defending Arkham Knight's depiction of asshole Batman essentially did the same thing as OP, pointing out it's established canon that he's a guy who'll get the job done, even if that makes him a bully. They weren't wrong, like OP isn't when defending the opposite.
Generally, and this is a personal preference, I'd rather have Batman be first and foremost a detective. He's also a martial artist, with all that entails: he's pretty deadly but that doesn't mean he has to use these skills because it's an easy way out. On the contrary, he should be about self-control: of his strength, his skills and his fear. He doesn't know a gazillion martial arts so he can break knees because fuck thugs. He knows them because they make him always prepared and whatever happens, he'll stay in control of a situation.
I know it's a chicken egg scenario but in that regard, I feel Morrison nails that take on the character, from JLA to his own Barman run and Final Crisis.
That's a character I like because he's smart and there's a genuine ambiguity about a dark guy operating outside the law and still being heroic and giving hope to others at the end of the day. Obviously, BB is my favorite movie depiction of the character.
On the other hand, I'm honestly not a fan of unironically violent vigilantes "because that's the world we live in", they always seem like a fast track to cheering for unnecessary use of lethal force.
