Re: Should Batman self narrate?
I actually don't recall there being that much narration in the "Arkham" games. Not in terms of internal monologues at least.
Batman describing the steps taken during 'Detective Mode' investigations was a necessary mechanic given the medium of being a video game but he didn't go on long diatribes about his psychology or his relationship to Gotham or whatever.
As for doing so in a film, I share the sentiment that it COULD be done well...but ultimately I'd pass on it.
If you want an example of how narration would go in a Batman film, it's simple. Just go watch the Bat In The Sun short films. "City of Scars," "Seeds of Arkham"...they use voice over narration for better or worse.