Mhhhm. I wonder if the big eyes are too replicate juvenile faces or if they occur because drawing the eyes of a face bigger than anatomically correct is just coming naturally and a purely stylistic choice since we focus most on the eyes of a human and thus our brains perceive them as bigger than they actually are. This characteristic of the human brain can be observed when amateurs/beginners try to draw even a non-stylized human face.

There might be a mix of both of these factors feeding into the style of anime but I personally don’t see all character-designs as immature. It mostly depends on the shape of the eye. Satsuki Kiryuin for example has very pointy eyelashes and Mako Mankanshoku, of the same anime, has very round, juvenile eyelashes and they make all the difference. To me at least.