I've seen my fair share of anime to understand why it hasn't become mainstream in American society. A large part of it has to do with changing people's preconceived notion that anime is a genre, when in fact it is more of a medium. We would never lump Casablanca, and The Three Stooges in a "Silver Screen" genre so it makes little sense to lump all animations together also. Although, there are sub-genres (i.e. fighting robots), which are unique to anime, upon closer inspection, all genres from horror to romance is represented in anime.
Anime as a Style
Anime is a medium, but to the confusion of many, it also represents a style much like how Film noir is tightly coupled to black and white film. The anime-style may include features like characters with large eyes and barbie-doll like body proportions, highly detailed technological objects, and excessive blood and violence. While these features may not be present in all anime, they are in enough of them to present an unhealthy stereotype for the mainstream American viewer.
Being an export of Japan, the stories told in anime often have Japanese cultural influences which do not always translate to American audiences. This is not so much an issue with anime as it is a result of writing stories for the Japanese market. Couple this with a healthy American entertainment industry where the audience never has to understand a foreign concept and you can see what an uphill battle it would be to get anime into the mainstream.
Crossing the cultural divide
Appleseed: Ex Machina is a wonderful film that is able to blend a style of anime into something not just palatable, but beautiful to Americans. The use of 3D computer graphics is akin to the many video game cutscenes we are used to seeing, but the use of cell shading for the characters' faces brings home this film's anime roots. The characters' eyes have been shrunken, while a prodigious use of motion capture really increases our sense of realism. Best of all, a talented team of American voice actors were given free reign to modify the script to suit American audiences. Never before have I wanted to listen to the "dubbed" version of an anime movie. However, I can't really call this dubbing as it is more of a transformation through dialog. Many of the lines of the movie has been completely changed to conform to American sensibilities.
It's all in the Woo
The biggest draw for Americans, may be John Woo's contribution to this film. Although Woo is known for his action, it is his combination of symbolism, character nuances, and cinematography
that makes him irreplaceable. When watching this movie, you really get a sense that this is much more than an action flick. You see the emotion connection between the characters without having it thrown in your face. All in all Woo is the final key in making this not just a good Japanese or American movie, but a great movie in general.
Here's the trailer: