The way I see it, The Batman is an origin story, albeit a different sort of origin from the kind we've seen before. This time round, we're not learning how he got the suit or the car or even the idea to become Batman - we're learning how he goes from a psychologically disturbed, violent, rage-driven vigilante to the master detective, great warrior and above all ''hero'' we're all familiar with. It is jarring to see Batman being so pissed off by an imprisoned Riddler that he loses control and slams his fist against the cell door shouting ''Why don't you die?'' (or whatever it is he says...can't quiet make it out properly). But that's the whole point of the exercise.
As far as Penguin does, I agree with you. Honestly, I had a bit of dissonance seeing Penguin sound like a street thug rather than the more aristocratic figure we're used to seeing him as. But I guess I'll get used to it.