Why do Spirited Away, Ponyo, and Arrietty have so much in common? I saw that Spirited Away, Ponyo and Arrietty, all written by Hayao Miyazaki, seem to have some common traits:


The hero is a girl.
Moreover, she is a girl who is special in some way.
She develops a friendship with a boy that is an "insider" and they help each other.
She seems to take a spiritual maturity journey while also building that friendship.


Is there some mystical connection to these themes or it is a mere coincidence? Can someone shed some light on this matter?
Miyazaki is often identified as a feminist. Almost all of his films have strong female protagonists, usually fairly young girls, and challenge traditional gender roles in anime. This presumably explains the first point.

As for the other three, I don't think these are particularly uncommon or difficult to explain. The protagonist in anime is usually somehow special, because a story about someone totally normal isn't usually going to be very interesting. Likewise, for the third point, most anime have some form of (possibly implied) romance, even in short movies. However, there's not a lot of room in movies to introduce extraneous characters, so the love interest has to be at least somewhat related to the plot. As for the final point, that's just another way of saying that it's a coming-of-age story, which is very common, especially with younger protagonists.

So other than the first point, I think these are just common anime tropes that you'd frequently see elsewhere, especially in other movies.