It may simply have to do with their characters. Like, Rarity actively tries to be better than she is, so she seems more human in that degree. The others simply have their own little quirks and ways of doing it. Twilight, for example, feels a strong need to be perfect. Naturally then she's not going to have the same sorts of conflicts as Rarity - where the core of Rarity's conflicts come down to her overcoming her nature, the core of Twilight's come down to her trying to correct a mistake or prevent something from happening. Rarity's conflicts are
internal, while Twi's are
external.
More to the point as you're likely talking about AJ, AJ's major flaw is that in spite of what it may seem she's actually a very introverted and perhaps even a tad selfish person. Not in the bad way, though, mind. She simply considers her actions and the ramifications thereof more readily than other's opinions. The Last Roundup incident is a perfect example of that. He very first thought was "I have failed". It was not, "What will the other ponies think of me, " It was not, "How will they react", it was "I have failed them. I have failed to meet my promise, and I must atone". A moments thought would have told her her friends wouldn't care, but she didn't consider their opinions. Instead, she immediately considered what SHE would do. She's an incredibly driven pony, but it's all internalized. She's driven to do what she thinks is right, but she's not good at looking outside of it. She's incapable of noticing how her actions affect other ponies when she has her mind set on something. As such, it's incredibly difficult for her to have internal conflict, or to even have conflict localized on her. Because she's driven to succeed no matter what, conflict around her is looney toons-esque, pounding her head against an issue and trying to solve it on her own. It's simply not the same sort of plots as Rarity has, and they aren't as 'human', because she's not the kind of person who realizes when she's doing something stupid. she needs to be
forced to see the error of her ways.
A large part of it is actually to do with the element of honesty. She simply can't conceive of doing wrong, so it doesn't occur to her that she is. I hate to apply the southern stereotype of narrow-mindedness, but it's extremely difficult for a pony like her to consider something outside her realm of thinking. As such, all of her conflicts and lessons sort of need to be external. Once the message is in there it
sticks, but it's got a damn hard time taking root.