Be sure to flesh out your ideas to a professional level you would expect from actual publishers if you want people to give actual constructive criticism on your ideas.
Otherwise they will just question the point of posting those.
I'll try to provide some regardless, just bear with it if it gets too scathing.
Just this week, I have thought of an idea for an interesting magical girl anime that I call Universal Lady Justice Aya. Like some animes such as Puella Magi and Utena, this is not a typical anime.
I don't understand what's not "typical" about the animes you've listed. They have moody atmospheres and alot of interesting ideas and underlying motives, but they are not exactly "Serial Experiments Lain" sort of deep cerebral experience. In fact, mood and atmosphere are what really makes them stand apart, which are quite common points for anime.
I think the term you've been searching for is "mainstream", which would sort of be true in that case.
It's more of science fiction vs fantasy.
Please, elaborate more on that. The text I've read below did not do anything to explain this. There was nothing said about the methods or reasons of the anti-magic organization. If they are opposed to magic in favor of technology you have to say why and make a reasonable argument to create a sense of conflict between the two.
I got the idea since in the usual animes, magical girls would often try to conceal themselves from the public. So I decided to work on that while dealing with breaking external and internal forces that drive people into lives and cycles of isolation, alienation, despair, and violence. Here's my synopsis:
I really quite like the way you worded that. That could actually make for a much more interesting dilemma. It honestly reminds me of superheroes and how their identities are a constant threat not only to themselves but also those close to them and how it can positively wreck their private life. Applying this to magical girls is actualy quite clever.
In the world, desperate girls have their pleas answered by finding white crystals and becoming magicals until until their lives are fulfilled. However, they have also become targets as worldwide anti-magical organization hunts them down. These such external dangers force these girls into hiding in a life of isolation and alienation.
Uh, why? I personally have problems when "evil organizations" get introduced, with no legitimate explanation of why they are being dicks. It's t he Captain Planet approach to antagonists, taking large, faceless and monolothic organizational structures and portraiting them as assholes for the sole reason of being assholes.
Furthermore, as I have said before, I dont really sense any conflict between magic and sci-fi, or even plain science there. It feels more like a conflict between idealism and cynism the way you explain it, though you can certainly apply it to those two elements.
Aya Masa, a girl isolated from the world by her protective mother, finds herself helpless at school and with her friends. This is until she finds a crystal and encounters another magical girl. Now a magical girl herself, she hopes to break the external and interal barrier of her life. As she does, she tries to free the abused, isloated, and dominated from their own cycles of suffering and bring justice to their oppressors. This is the epic story of a girl who brings hope to those under the shadow of despair.
Sounds like a good setup for a main character. Exploring the aspect of isolation and alienation from and through society in family and at school through the eyes of somebody going right through it is wonderful if done right.
Hell, if I were you I would do a full-blown unreliable storytelling, Pan's Labyrinth style. You should watch that movie. It handles the exact theme of magic vs reality and leaves it up for the viewer to interprete it's events while being whimsy, imaginative but also cruel and gritty at the same time.