The original is more of a love letter to technology [SPOILER] and ends with the first merge of human and AI in to something new [/SPOILER] (it's not about technophobic humans policing the bad runaway machines).
American live action Death Note was the same: I was hopeful since they cast Willem Dafoe and he's usually in good stuff, but no, it was also pretty bad. It seems like American film companies are just trying to capitalize on the popularity of anime without grokking what made the best anime great.
Both films mentioned were commercial successes, but I think in the long run they burned audiences for this sort of film. I won't see any more American remakes of anime for some time.
Don't bet on it. Also the live action Akira is currently on hold, but Taika still seems keen to do it.
The other American live-action remakes mentioned were profitable, but by much more narrow margins. If what people are saying about it being truer to the source material is true, then it seems that producing better remakes does in fact produce greater profits. We only have a narrow data set to look at for this, though.
I really don't know what a live action Akira would look like. The body horror scenes are going to have to be CGI, which could go really badly.
J. J. Abrams is the living embodiment of this approach, which is why his Star Trek and Star Wars movies look gorgeous and individual scenes are awe inspiring, and the overarching story arcs are all fantastic on paper, but the world building and and actual in-world logic of the setting or character decisions in it just don't make any sense whatsoever. Zack Snyder is just as bad.
But now they've devolved into beautiful looking action movies which exist just for the sake of action, with the story being secondary.
I’d probably suggest Rurouni Kenshin (Samurai X) or Gundam Zeta instead. They have interesting themes, are more adult and have amazing art.
The Patlabor TV show is definitely much lighter material, a lot more accessible to children.
I think maybe it's the high-concept, almost frightening, aspects of GITS that resonated with me. But I understand why it's not popular with most people.
Obligatory Patlabor 2 opening title sequence: https://www.youtube.com/watch?v=IsMTpSDAGxM
Patlabor is slow, sure, and purposefully so (it has and deserves the reputation as being the "boring" mecha show), but cheezy? I haven't seen the TV show which I hear is a lot more comic, but I wouldn't call the original OVA/first 2 movies cheezy.
NGE can be philosophically heavy at times but is too diluted by its action sequences and fan service moments.
The first GITS movie is a philosophical tour de force and a piece of art that transcends time. A masterpiece.
It may also be that a lot of anime are series, and require a time investment.
The only other (comparable) anime that jumps to mind and something I can definitely recommend to you, is Serial Experiments Lain.
Wikipedia link (warning: spoilers ahoy): https://en.wikipedia.org/wiki/Paranoia_Agent