I'll say this, these films are sorely lacking in Bruce's other personas... like Matches Malone. Something like that would have been perfect for saving Reese and that whole thing with the sniper team and attack on Gordon in TDK. The absence of those features is yet another indication that Nolan's Batman is not the detective his comic counterpart is.
I was saying the exact same thing a couple of months ago in a thread, not so much the Reese rescue scene, but the other scene with the blindfolded cops. Going in there as Bruce Wayne with no disguise was dumb. I also suggested a Matches Malone type disguise would have been ideal for that scene, because it would have been so easy for the cops not have been blindfolded, and what's he gonna say, 'Em, hi, as you know I'm the famous Bruce Wayne, just looking for a toilet!'
But, I don't see that it should be *that* much of a problem having Batman in costume out there during the day. Of course Nolan was probably hesitant in case he looked a little silly standing out in the sun in a big hefty outfit, losing some of the mystique as well. But if it is shot the right way, he can still carry the same mystique and gravitas.
The Reese rescue scene, shot the way it was, could just as easily have been done with the Tumbler, with BM driving off without getting out of the car, that is, if it had not been blown up! So, there is some logic there for BM not making an appearance, and Bruce's cover story was fine I thought, it was also nice to see the exchange of looks between Bruce and Reese.
I guess Nolan did not go for the Matches Malone type disguises as, y'know, they can look silly on film, they can look a bit 'joke shop'. But he could even have had Bruce go in to the blindfolded cops with a small crash helmet on(as he just arrived there by bike). He goes to too much trouble protecting his ID to just go walking into crime scenes, where you might expect action, as Bruce Wayne.
edit: and that scene was all about stealth, so having Batman in his outfit during the day was not really viable, some kind of disguise should have been used though.