In the case of schoolgirls -
I suppose with some authors or creators, it's because they're not schoolgirls.
If you're an older male writer (or even college age), I can see where you'd struggle to write school-age girls as either -
1 - You've graduated a while ago
2 - You aren't a girl and thus grew up not doing the same things or going through the same experiences that a Japanese schoolgirl would, the same as normal highschool boys don't sit in circles and whisper about who they like (I think) or worry about their hair or clothing. (I'm just going by the general idea of highschool, I don't mean to offend) Plus, girls have things that guys don't, including stereotypes, which are ever-present in most schools. (They were in mine -we were still a very accepting school, but we still fit into boys and girls personalities.)
3 - Making schoolchildren do accurate schoolchildren things isn't on the top of their list. In most "highschool" animes, from what I see, they don't make Haruto worry about getting his Physics homework done or follow Haruka's adventures in eating cafeteria food, going to band lessons and listening to Foreign Language lectures. Most times they go on daring journey's fight the bad guy and look awesome.
I'm not saying that there can't be any well-rounded women - and maybe someday, there will be a balance between the boys and the girls where they both go about normal life, but in an entertaining and satisfying way (which I would totally watch). It's just not here yet.
As for other anime, it might just be for the same reasons, plus, the audience seems okay with what they have now, but if someone does make a new manga with a well constructed female character, i'm sure they would buy it from interest as well as something new and entertaining, whether the characters are normal or have some sort of other-worldly power.
Also, just as a note - big eyes are a staple of anime. Not all have it, but it's hugely popular for the girls (and some boys too) to have large and shiny eyes because that's how it's been for a long time. There are lots of exceptions, but i'm just naming the bulk.