They could not deviate to the other side of the street because it was not blocked. Diverting down to Lower Wacker was the only available option.
I see emergency vehicles driving on the wrong side of the road almost every day. They teach people in driver's ed, and you must know to get your licence, to get out of the way of emergency vehicles and pull over.
I guess no one in Gotham knows to do this.
It's not my biggest nit pick of the film, but it does reak of a forced "because the script needed it" encounter. There probably is cars just barely at the top of the frame, but if so, that's poor composition and/or planning on Nolan's part. Or probably just one of those mistakes that happen, Nolan cursed himself, and decided it was too expensive to reshoot...then thought no one would notice or care.
How little he knows of the anal retentive, internet Batman nerds!