I sometimes think when it comes to defining Mary Sues, it’s sometimes used to disparage characters that unfairly get this (especially Carol Danvers). I actually think she’s not a Mary Sue because she’s been a punching bag (especially for villains and Rogue, and to some extent the writers themselves) for so long that it’s about time to treat her kindly and respectfully. Giving characters flaws and consequences for their actions is the easy one.
Sometimes some characters are Mary Sue because authors won’t take them to where they’d logically become. This isn’t always the case but a surefire sign especially if authors like this character a lot as to avoid taking them to the logical option. I actually think that’s the case with Kitty Pryde where writers seem to like her a lot but to the point of avoiding what she could logically do. If true, this would make the Age of Apocalypse portrayal as assassin the least Mary Sue she’s been.
In the sense of focusing a lot more on stealth and assassination in tandem with a feline nature (retractile claws and going through narrow spaces) that it’s appropriate for her. It would just as appropriate for her to become the character Psylocke ended up as. Psylocke, as initially presented, was a white woman who certainly hadn’t any ninja training until she traded bodies with another woman. Kitty got brainwashed to do ninja stuff and would easily do the things Psylocke ended up doing.
In a way should she use the focused totality of her phasing powers when she’s about to assasinate enemies. Actually she’d also make both Feral and X23 redundant if only writers stuck to giving her claws and that she’s already got a feline name that she’d actually be Feral (there are some attempts at making her more feline). Some stories do treat her as a female Wolverine, right before X23 came into being.
That she’s closely associated with Wolverine still makes me think she’d have no issues with stabbing people brutally (again she’d make both Psylocke and X23 redundant if they let her become a clawed asssasin). Likewise writers are often tempted to make Tim Drake evil. It’s not that he lacks flaws but if he’s intended to be likable that makes it harder for some people to trust him. Especially if it feels manipulative that Tim Drake being shady is understandable.
It’s not that he should become evil. I’d rather have him do things that he thinks seems good but bothers people (just like in the real world). Something like poisoning animals to keep them from attacking him but ends up angering Stephanie a lot. (It could happen though.) That would mean even if Tim meant well, he’d become responsible for his own actions should it bother others.
Even if Tim isn’t evil, given the repeated attempts at making him so having him do shady things to do what seems good to him does make him less of a Mary Sue. But in the sense of facing the consequences for his actions, especially if it angers people like his girlfriend. Though that would mean either writers have spoilt him a lot or that Tim would have to actually have some unlikable tendencies to do what he thinks is good.
(Like everybody else.)
As for Barry Allen, whether if he’s a Mary Sue or not’s up to anybody’s guess. The real issue isn’t so much that he lacks a personality but rather he lacks a personality beyond being an idealised reader surrogate. Make him more than that and some readers would take issue with it. Again it’s not that he lacks flaws and personality but that the real issue’s that he’s so stuck in the idealised fanboy role that it’s about time to go beyond it.
Not so much to become unrecognisable though I think if people were to turn him into a surrogate for either Red Riding Hood or arguably Dante that Barry would inevitably develop his own mind either way anyways. In the sense of what else they can do about him other than doing super speed feats. Though that would necessitate going by whatever’s logically expected in a story.
As well as having to tone down the speed feats or at least provide realistic consequences (though writers tried). Something like that he can run as fast as a van, which’s highly plausible as well as no phasing, tornadoes and the like. In fact he could easily be an escape artist if only writers let him be. (Again that would necessitate having him go where he’s logically expected to.)
Something like Caitlin’s now a werewolf and she’s about to attack him. If noboby wants Barry to kill her, he might as well con her as to allow himself to escape in time or even before that. I actually think the tendency to make him so OP might be partly because having him become an escapologist wouldn’t just necessitate writers to tone it down.