In addition to all those shows about high schools and moe, there are dramas about boxers and baseball players. Bizarre psychological thrillers. Supernatural detectives. Slice of life like the currently trending comic Silver Spoon, which is getting an anime adaption (city student goes to agricultural school, experiences culture shock and rethinks life).
People go where the content is. You can find certain kinds of storytelling in anime that you can't quite replicate anywhere else. The fact that it's animated leads to flexibility that's difficult with live action due to practical matters like actor contracts and being able to afford sufficient cast members for certain scenarios. In the west animation is still seen for the most part as children's cartoons and low-budget animated comedies for prime time on Fox. As we've unfortunately seen, outside of The Last Airbender franchise, dramatic and action-adventure animation has a lot of trouble gaining traction in North America - fallen flags like Young Justice, Tron Uprising, and even shows like Motorcity and more cartoony Green Lantern: The Animated Series.
As an example people are going crazy for Game of Thrones right now because, in part, it's still uncommon to see fearless and ruthless storytelling in live action TV series - especially stories that require a cast of dozens and where anyone can die without warning.
That sort of thing is much more common in dramatic animation leading to interesting and unpredictable storytelling.
The thing that does hold a lot of western viewers back from anime I would say, is the harsh transition to another culture's standards for dialog, timing, comedy, and mannerisms. Even in purely dramatic shows and films, these things can still throw a lot of people at first.
