one of the more interesting parts of the barbie movie i think is the presence of weird barbie, actually. like yes, the kens serve to show how women being in power isn't actually that much better than men being in power, because consolidating all that power in one group means the other becomes disenfranchised and lower status or class by default. but there are also interesting things to be said about femininity and the way this movie addresses it!
like, look at every single barbie and you'll find a lot of extremely feminine women. yes, they win nobel prizes for literature and they're scientists and they have a whole range of skills. but they're all also conventionally attractive and feminine, for the most part -- excluding that one line about "you're a physicist, do you want some pants?" (very odd, bc it's not as if scientifically inclined women cannot also be effeminate, but that's a whole other point i'm not going to get into right now.)
the only one who is not stunning, who is not put together, is weird barbie. and despite her status as part of the socially established higher class via being a barbie instead of a ken, she is still ostracized, because her version of being a barbie is not what is expected of the group. she does not comply with the guidelines and rules and structure of femininity. sure, she has a dream house, but it's away from everyone else. sure, she's a barbie, but everyone calls her weird and stays away from her, and she's a sort of old wives' tale about what could go wrong.
while she may receive some benefits of being a barbie, i.e. a woman, in this hierarchical structure, she does not receive all or even most of them -- because she performs it incorrectly. (aside: i wish they hadn't cleaned her up and made her into an attempt at hot alt pink fashion toward the end. when she's more put together, she loses a lot of what makes her special, i think.)
allan fills a similar niche, in that he is neither allowed a place within the power structure when the barbies are in control nor when the kens are. he is a man, as far as we know, but he is not a ken. and because he is not performing his identity in the ken-approved way, he does not reap the benefits when they take over. he continues to exist as lesser, and aligns himself with the barbies.
i suppose the point i'm trying to make is that both weird barbie and allan serve an important role in this movie in pointing out the ways that those who exist outside of perceived binaries or structures are still yet harmed or disenfranchised by the enforcement of them. if that makes any sense at all.