Exactly!!!
If this man feels he told his story after 3 films then move on to something else. IN 71 years this character has had dozens of interpretations all with their own level of success. Matter of fact in the 22 years I've been reading the comics that's always been the greatest appeal to the comics to me. I get to read so many different versions of Batman that all keep the principle themes intact that it's a blast.
The movie series by WB has also been reflective of that with Burton, Schumacher and Nolan all bringing their own flavor and ideas with the same characters. Would be a shame to see that end just because they decide to stick with and possibly also hinder one specific vision. New director should bring his own flavor and ideas to the table not be restricted by the creations of the previous. Now if it's with subtle and vague references like what Batman Forever did with it's predecessors it's not too bad but I rather something completely fresh.
I believe this post helps explain what I'm going to say.
Nolan's story is the events of these 3 films, not the events after his 3 films. It wouldn't be that hard either. Have the new trilogy set after the events of Nolan's films, starting their own arc. Just don't contradict the events of Nolan's films (ex. resurrecting Two-Face), and you can have Gotham look different, the characters played different, etc. That way people can have both a continuation of Nolan's films if they please, or if they don't like that then they can just assume that the films are part of a different universe. It's a win-win and wouldn't be that hard to pull off.
Batman Forever was sequel with a similar continuity, but a different feel to it.
I think a new vision would be good. Barring that Nolan doesn't do anything
that significant that would make it difficult to continue the Batman film series (In which I doubt WB would let him do. They want the cash cow to keep going after the next one), Nolan has set up a universe that can be blown up in scope if possible.
I believe that a new director should not destroy realism, but slowly expand audiences suspension of disbelief slowly. Nolan's "realism" is based on how the world would really feel about Batman, now the next the "arc" should be used to a world with Batman, which opens up to more great stories.
Personally, I always believe that the status quo should constantly change from film to film so I would love to see a villain that can simultaneously crossfade (if that makes sense) Nolan's vision into a new vision. I don't think it should abrupt like it was from Batman Returns to Batman Forever. The first two Batman films obviously show an inexperienced Batman (I still feel like Batman wasn't fully the Batman we know in TDK), so I hope by the end of Nolan's trilogy we see the Batman everyone knows and loves.
I like Nolan, but I know there are many things a new director can improve upon, like fighting, Batman's detective skills, and maybe using more of his skills that haven't been used yet, like his tracking skills, his disguise skills, or his escape artist skills.
At the same time, like Vulcun said, don't contradict the other Batman films. Don't create continuity nightmares and push the GA away. People aren't kind to reboots.
Keep in mind that the new director could possibly use Joker, and I will admit that would be a pretty ballsy move if they did use the Joker for the 4 or 5 Batman film.