One of the most common complaints I've heard targeted towards AAI2 is the overload of characters accompanying Edgeworth throughout the game, unfortunately leading to situations where characters repeat each others' lines thus creating a lot of unnecessary padding (and the game is already loooong). Gumshoe and Kay are the biggest culprits in this regard but Ray, being the guy who blends into the sack pretty easily, is also not far off from being one as well. I've heard people say that Ray was a pretty useless assistant outside of AAI2-3 and being the one Edgeworth can run into when he's in a jam. Personally, I think he had a lot of potential but the writers missed the opportunity to expand on his character due to the aforementioned problem with the game.

And this is where we run into Kay. Her arc was done in the first game. Done. She had no good reason to be in the second game apart from fulfilling the role of the mandatory sidekick teenage girl and pressing a few buttons on a device with no special skills whatsoever. This is why I prefer Maya, Ema and Pearls (pre-DD) over her because they are trained in what they do and using or failing those skills is part of their character development. Kay on the other hand, goes on about stealing and stealing and her major achievement in AAI2 was "stealing" back John from the clutches of a fridge after reported missing. But guess what? This is what the police normally does after someone is reported missing and Gumshoe was accompanying her so her stealing skills are nothing of importance. Gumshoe's role was also greatly downgraded due to Kay's presence.
Also I never got the thing with her wanting to steal "the truth". The only situation I can think of where that expression is actually applicable is when you steal secret documents alongside becoming a whistleblower. Granted, AAI2 came out before the Snowden case but I only started playing the Investigations series last year and frankly, I was disappointed that the games didn't explore stealing in a more morally questionable way. It was the modus operandi of the previous Yatagarasu to do just what Snowden did but unfortunately their successor only steals lines from Edgeworth while "stealing" for her is clearly a synonym for "obtaining" that she uses just to stir up some feelings. She's just a good girl and Edgeworth will have a super easy time explaining to everyone about the time when he worked with a self-proclaimed thief on cases Yeah, especially after all that history with forging evidence and manipulating witnesses. It will fly past anyone just dandy~

Yes, but there's the Forgotten Turnabout which is all about her. Except it wasn't really about -her- because anyone with amnesia could've filled her shoes and it'd have no effect on the case whatsoever. It was like an episode of Pokemon and in the next one they pretend nothing really happened; just a temporary stumbling block. I personally would've preferred for Gumshoe to take the fall instead and have both Edgeworth and him reminiscence about their working relationship throughout the years because that's something we've witnessed to some extent and it's had its ups and downs. Now that would've been a treat to long-time AA fans and a way to reward us for sticking with the franchise for so many years. Instead, Edgeworth consoles poor Kay with what could be summed up in this phrase "You're the Great thief Yatagarasu. It has the word "great" in it so that means you're a great person". But imagine if Gumshoe took her spot and they'd talk about the times when Gumshoe resigned just so he could follow suit with Edgeworth and with each whipping from Franziska, he'd start to remember her more but yet struggles to remember his memories with Edgeworth and gets all teary-eyed over it. And at the end of it Edgeworth's and Gumshoe's partnership would be stronger than ever and you'd actually sense it for once. If I had all the time in the world I would write an AU fic where this happens.

Also, Edgeworth's just not the type to warm up to a goofy teenage thief girl within the time span of two weeks. Compare Edgeworth's relationship with Gumshoe in AAI-4/AA3-4 and AA1-5: It probably took years for them to reach a stage where Edgeworth actually gave a damn about Gumshoe as a working partner yet he still compares him to a gum stuck on a shoe. Kay does exactly the same things as Gumshoe, constantly interrupting and bantering, yet he doesn't seem to mind her company in crime scenes when it's clear that Ray and Franziska could've been as capable in assisting him and Ray at least would've been far less intrusive. But with Kay it's all moonlight and roses just a week after they met. I miss Edgeworth when he was more socially awkward. I don't think his transition to protagonist should've changed him too much despite him clearly needing some developing after all he's been through.