Well, in YEAR ONE.....Jim Gordon had just transferred from Chi-town. He was freash off the train, and had been introduced to Gotham hardcore style firsthand with Flass as his tour guide. But, he still wanted to believe in the GCPD. He was new, and he thought he could get it done without outside help (the Batman). But, over time....he pretty much got "it" and understood, alot like Batman did, that you can't do it alone....you need help. So, he needed more time to actually be okay with the idea of teaming up with a vigilante. And, plus....he had had some major problems in Chicago with the Police Department. So, the last thing he wanted to do was **** up again with the PD this time around.
In Batman Begins, he's lived in Gotham for a lot longer. In the novel, he'd left Chicago and come to Gotham too.....but not during Batman's first year, but alot closer to the Wayne's Murder. So, he'd been in Gotham for so long, his spirit had been beat down already. He saw no way out, at all. He had no trust, no belief in the PD, and knew there was really no hope. Ie: "who's there to rat to, anyway?" so....he feels alone. A hell of alot alone than YEAR ONE Jim. So, by the time Batman comes around...he's open to helping him, b/c there's no other alternative. After Falcone being handed over by Bats, he doesn't even think about arresting Bats. We already know he's on Batman's side by the morning after Falcone's been arrested.
So, really.....at no point, does Gordon actually see Batman as a threat, atleast nowhere near the way he did in Y1. So, him trying to find out Bats identity would kinda be against how he's acting.
And, I think the subplot would have really slowed and hindered the flick. Once he becomes Batman, it's a fast moving train through the story. And, really....he wasn't Batman for a full year. Gordon would have to investigate and get that close in almost a week or so.
