You're right, but I also see in Beckett's character the need to take on bigger challenges and that's what DC offers her.
See, but that's just what I think is out of character. The Kate Beckett I've known for five years would be offended at the suggestion that solving individual murders and helping the victims' families get closure is in any way "small." She would insist that it's a vitally important job, as important as anything else.
I mean, Beckett is basically Batman. She suffered a childhood tragedy that compelled her to fight for the victims of crime. Now, okay, maybe Batman did join the Justice League and occasionally battles alien invaders and space gods and immortal cavemen, but there's no way he'd give up patrolling the streets of Gotham and saving ordinary citizens from street-level crime because it wasn't a big enough challenge to suit his career ambitions. Because what he does is not about himself; it's about the people he's fighting for. And Beckett is the same way, at least when she's written in character.
DC is also a much better setting for the overarching story of her mother's murder. She is more likely to find something to take down senator whatshisname in DC.
And I'm rarely as invested in this show's overarching story arcs as I am in the weekly mystery-solving and character interplay. So that's not a direction I'd be eager to see the show go in.