Well yeah, that's why most of these writers are writing superhero comics for kids instead of serious crime novels
Any of Loeb's writing isn't really a good example of what comic Batman is capable of. Those stories are infamously dumb/style over substance and picked apart accordingly. Loeb's Batman couldn't detect his way out of a paper bag. The likes of Morrison and Dini are perhaps better at displaying what he is capable of, even if in a primarily action/adventure capacity that doesn't get too complicated (because the genre is superhero comics). Or Doug Moench's "the Forensic Files of the Batman," or a lot of the arcs in the original "Legends of the Dark Knight" series. Even if he doesn't 100% live up to the moniker, basic fact checking is well in his wheelhouse, which he doesn't do here while he's plotting not only to take down someone who hasn't done anything, but to murder said person. If the point is that this is deliberately OOC for Batman, it's because the film is relying on us to have prior attachment and knowledge to him. We are informed that his brutality is new, but not shown and this is the first time we are seeing this version, we have no reason to think he's ever been anything but a psycho who doesn't put much effort into detecting anything.
Basically, it's using bad writing elsewhere to excuse bad writing here. When in reality, both instances suck.