Xion and Kairi fall into those stereotypes. Don't you think?
Namine too, to be honest. Although I think those two are given a little more freedom by the narrative than Xion.
While Kairi in KH1 was pretty damsely (she gets a 'moment to shine' and save you, but then fades into the background again), I really liked how in KH2, it's Namine who saves her from the cage. You don't get a lot of women saving women, really. And while Riku does have to protect her from Saix, after that, he gives her a Keyblade and she does join in to help! And she sticks with you until the very final boss, unlike in KH1, when she just stands around in Traverse Town with pep talk dialogue and given nothing else to do by the narrative. (Because Riku took over her role as the damsel for the very last part of the game LOL oh KH)
Then again, I can enjoy Kairi's KH1 role without getting all that frustrated because it's so obviously a reference to the classic Disney tropes, so it does kind of fit with the fairy tale atmopshere of the game. Not that I would defend it based on that! It's just why it doesn't bother me so much, I guess. I know they didn't HAVE to go with that, and especially when there is such a tiny number of girls in KH to begin with, it is kinda grating to waste them with cliches like that. (Kairi was the ONLY named original female in KH1, and surprise! She's the damsel!)
Namine is definitely very damsely in COM, even with the subversions going on. Yes, she was the one manipulating Sora's memories all along, but she was being forced to do it and was clearly unhappy and considered an object (tool, weapon) by the Organisation. And even when we find out that Sora's 'save the damsel!' plot has a twist, the plot still has Axel set her free before she can do anything. And then Marluxia captures her again at the end... But, I actually like the way they handle Namine. It feels to me like it is acknowledging the unique pressures of women like her who are thrown into scary combat situations, and gives her a chance to develop her own strengths and ways of resolving issues that aren't blunt force.
Then we have Xion... she's meant to be a fighter from the start, unlike the other girls, but iirc she goes missing from the Org three times, and twice she is knocked out and brought back forcibly, the last time so that she can be transformed into the second-last boss and killed. (And the first time, that veil lizard knocks her out and she lies unconscious while you fight to save her.) (Not to mention the other times she lies around being unconscious to fuel Roxas' manpain.) Xion goes in and out of damselhood so many times over the course of that game, I guess that's why it stands out more. (And her actually being that Euthanised Damsel, the creepiest of all the damsel tropes, stands out too.)
Luckily, we haven't had a 'save Kairi' objective since Namine freed her from that cage, I don't think, and Aqua is amazing, so let's just hope with all our hearts that Kairi gets her own back in a new title soon!!