I was actually quite sad that this was taken out of the animated adaptation of The Dark Knight Returns. It's really the heart and soul of the book - and that goes for many other Batman books. The greats. Peter Weller could have gotten way into it and given us a gripping look at Batman's psyche.
There's something about getting into his head and really just feeling like... this is what it feels like to be Batman. This is what it feels like to -see- and -think- from inside his head.
It adds a whole new layer to the detectivey stuff, but also the combat. Instead of just cool wham-bam I'm a ninja stuff, it becomes deeply surgical and intelligent. The perspective it adds emphasizes it more than simply showing it. I feel like it provides Batman half of his personality, and that Batman's personality is sometimes missing from the existing films.
Then again, it's also a spectacle seeing a silent, steady, spooky, dark-silhouette Batman who isn't saying anything...
Are there other ways to get it across than self-narration? It's possible.
Is self-narration inherently corny? I think it's all in the quality of the writing.
Another example: RDJ's Sherlock Holmes (even though I prefer Mr. Cumberbatch, but that's beside the point).