I'd argue that there is no real arc in this series, films one and two work independently of each other. And who to say Nolan would even close any doors in film three?
There's a fairly clear arc for the character of Batman.
BB is about Bruce discovering his calling to protect the innocent and keep everyone from the pain he suffered. It goes through him learning all the tools, and what he needs to know, to form Batman. It then goes into him becoming Batman, and his struggles to finally establish Batman in Gotham.
TDK is about Bruce Wayne, already established as Batman, slowly realizing that fixing Gotham, and being Batman, is not going to be a short term thing. It's also about him fully realizing the challenges being Batman presents him with, and what kind of men he's going to have to fight while being Batman. It's also about him realizing that he has to be prepared to do almost anything to protect Gotham as Batman, even condemn himself in the public's eyes.
On a more basic trend, it's following the well used theme of
Young man becomes hero, struggles, learns, and grows and finally establishes himself as hero.
Established hero is discontent with reality of what he is and what he may have to stay, and with all he may have to give up to be a hero, as well as the struggles of a dual life.
Going with this theme, the next logical step (and the step that is usually done in an arc like this) would be the hero coming fully to terms with all he has to give up, completely accepting his role, and settling into a normal balance between his two identities.
