The reasons of comedy and drama, as described by Word of God in cde's answer, are clearly the most important. Diverse cast of Riley's emotions makes the movie more interesting.
I would like to add three complementary points no one else mentioned:
Once we assume that all emotions in one's head must have gender and it must be similar to person's assigned gender, we start slipping into deep sexist swamp where only "Woman's Tears", "Man's Rage" and other non-objective abominations dwell.
Fortunately, Inside Out is far from being sexist. While Riley has some stereotypical "girlish" traits, they are affectionately deconstructed all the time. Moreover, Riley is shown as a plucky, independent girl: she plays hockey, talks back to her parents, and her inner life is not limited to Imaginary Boyfriend Machine.
Note that Riley's Sadness looks like a daughter of mom's Sadness, and Riley's Anger is a younger version of dad's Anger, sans the moustache. It can emphasize the fact that Riley has inherited the traits of both of her parents. Her dad taught her how to be fair and assertive, and her mom taught her how to understand other people.
3. Main vs supporting emotions
While Riley has all kinds of "men", "women" and "monsters" in her head, her two most important emotions are Joy and Sadness, who are "female". They are her avatars in her inner journey; and the three remaining emotions, Fear, Anger and Disgust, serve their role only in specific situations (eating broccoli, playing hockey, dealing with electric cables). Their attempt to drive Riley for a prolonged period of time was a desperate measure and almost led to a disaster.
It's arguably easy to imagine "female" Fear and "male" Disgust, or even "female" Anger similar to mom's. But imagine for a second that either Joy or Sadness is "male". Or even both. That would raise a lot more questions.
So, while diversity is respected and silly gender stereotypes are mocked, Riley is still a vanilla cisgender girl. She is not exactly an old-style Disney princess, but on the other hand she is not an asexual introvert, or a crossdresser, or into hairy guys. See? Nothing to worry about.