This is not a good idea. Nolan is a brilliant director and there's no denying that the man delivered at least two of the best superhero films ever made. No one is going to argue that DC's films need a jolt in the arm either, but there are some very concerning problems with Nolan overseeing and defining the DC universe on film. These are those problems. Problems I'd be happy to be entirely wrong about.
This isn't Batman
Nolan is all about reality and tone. Even in his more fantastical films everything is very grounded. It worked great for Batman because the character of Batman can go there. A large chunk of the DC Universe cannot, especially when you're talking about films in which a bunch of heroes team up and do really outlandish superhero things. If we judge from the trailers of Superman, which Nolan had a hand in, then a serious, "realistic" tone is what he's driving for with the DC films. Does it look like it could work with Superman? Yes, but pushing that thematic tone across the board is just a recipe for disaster. It's great to have a different tone from Marvel's films, but there's a reason Marvel's films work so well and are insanely popular.
He isn't Joss Whedon
I don't want this to turn into a Joss Whedon versus Christopher Nolan piece so I'll also say he isn't J.J. Abrams either. What do those two directors have in common? They've created epic story arcs with massive amounts of characters that stretch across multiple seasons or movies. It's hard to imagine Nolan pulling it together as well when his only story that's moved past a single movie is Batman and by the third film there were some serious issues in the world's plausibility. Obviously no one is perfect, but doing what Marvel has done over Phase 1 takes a skilled hand that DC has already shown it doesn't actually have and Nolan doesn't have the credentials for. Nolan definitely has awesome ideas, but he hasn't shown that he is capable of creating awesome universes. There's a big difference between making a movie with a cool premise like Memento or Inception and building an entire universe within a series of films.
It Means Less Original Nolan Content
To that point: if Nolan is focusing on a bunch of movies that aren't even his own then that means we get less Nolan movies. Not doing one awesome thing because it prohibits you from doing another awesome thing is kind of a dumb argument, but in this case it's entirely valid because Nolan's best work is when he takes an original concept and turns it into a movie like we've never seen before. No offense to whatever directors will be helming DC's films under him, but they aren't going to deliver anything close to the awesomeness that is an original Nolan film. More DC universe wrangling is just going to mean less writing and directing... unless he secretly has a twin and that's how he does all these amazing things.
It Could Ruin the Nolan Brand
Right now Christopher Nolan is the shit. He could walk into Warner Bros. and say that he wants to film a man taking a two hour dump and they'd green light it. At the moment Nolan's name on something means its going to be good. That could seriously change, especially if WB/DC still don't have their act together. The JLA screenplay is falling to pieces and they're going about constructing the DC film universe in reverse order and with no coherent plan as of yet. Nolan is the man they're bringing in to fix this, but if they're still messing things up (or my previous points are true) then he's not going to be able to and his name is going to get stuck to a lot of crap and possibly another failure by DC/WB to capitalize on their insanely recognizable characters. There goes Nolan's two hour epic Man on Pooper.
This isn't the Director You're Looking For
Nolan did incredible things with the Batman franchise, but he wasn't really a Batman fan beforehand nor was he really a comic book fan. His brother, who helped him write the screenplays was, but Nolan has been noted as saying that he basically used the comics as a blueprint and extrapolated from there. This worked great for the Joker, but for an entire universe its going to start pissing people off. Yes, you can learn the history of these characters, but it doesn't create the same passion as growing up with them. He isn't invested in the decades of character history and fandom. To do what Marvel has done with their characters -- walk the line between rebirth and fan service -- you have to be. Of course DC relaunched all its books recently so this argument may sound a bit moot, but I'd still want someone who has been invested in comics and superheroes his entire life to steer my iconic universe of heroes. Nolan may make many of DC's characters interesting, but it may not be in the ways we want.