The initial Barbieland is depicted as an inverse society where Barbie’s are in power and Ken’s are just there as an addendum (way less toxic than reality yes, because it’s toy world not real world).
Then after contact with the real world, Ken completely misrepresents reality in his toy/simplistic way, and tries to implement it in Barbieland, with the objective that if he does so he will be able to be with the sole reason for his existence. That pain is also explored.
Finally, after some talks, the conclusion that Ken can be his own person is reached, this is not that developed because the movie is about Barbie ffs.
To me personally, the Kens were initially a simplistic depiction of women in the real world, which then gets tangled up with the actual real world, and end up with some societal progress for the Kens, albeit small, and a huge emotional progress for them.
It’s normal that their societal progress is small, since women in the real world didn’t get the rights they have from day to night.