I'm sure. I mean, there's no inherent reason these privileges should accompany any sort of bad personality traits.
But they serve to interrupt the feedback loop both socially and in life in general. If we take any examples, like mine or a pretty privilege or a wealth privilege, and we look at how life plays out, you're more able to do wrong or perform poorly without the consequences of it.
Lord knows there are plenty of people who were born into wealth and are able to notch some accolades that most people can't because of it, and they then think they're geniuses. They avoided the normal course of trial and error that would show them exactly how incompetent or wrongheaded they are.
A woman with pretty privilege, or any other sexually valuable person, can be vapid, selfish, or even cruel, and people will put up with them just because. Otherwise, these behaviors would be met with criticism and rejection.
So, not to rant on forever, but I think you can very much be a good person while having these privileges, it just glosses over the normal system of consequences (feedback) blinding the individual to whatever badness they might naturally be susceptible to engaging in.
I'm 100% going to flesh this idea (the dangers of privilege) out into a full article now, and I owe you for that. Thank you for asking such good questions. You're always making me think!