Maybe because it isn’t done to death? Think about it. You watch a cop show. They follow the rules of cop shows. Same with horror movies and psychological thrillers on screen. There was actually a movie about it. I think it was called ‘The Cabin’ and it make up a story about why all the plots follow the same rules.
Anime is from a different culture we don’t understand therefore we don’t see things coming. Watching something like anime you have no idea what’s going to happen next because we don’t know (or at least I don’t know) the conventions. In the west Inyuasha’s brother would have become ok with the fact that his sword let him heal people but not kill them. I didn’t see all of the episodes but I think I saw a fair number. There were a ton though and adult swim kept replaying the same three or four so don’t quote me.
Also anime characters (and cartoon characters in general) can be profoundly touching in a way that real life actors can’t. Spike from Cowboy Bebop is Spike from Cowboy Bebop. You don’t see him in another series playing a chuckold husband or something. In a cartoon people and places can be reproduced in a way that’s impossible to do in real life even with CGI.
I think you want to see a world where you could go out and use your aggressive tendencies and be rewarded for doing so. You want to be the top predator? Well here’s a world where that’s possible and it actually looks like a nice place to live because you don’t see the squalid filth that an at war society would be portrayed with in real life. You just see a samurai with his sword next to a picturesque field and not all the sweat and dirt because he hasn’t gotten to bath in over a month on the road. You get imaginary worlds that look like somewhere you want to live and cultures that you want to participate in.
I think that the reason you found it in anime in particular is because all (or almost all) of the girls in my high school liked anime and guys seemed to like it too so it’s right around your age range. It just came into your life at a time (I’m guessing) that your aggressive tendencies started to mature, you mind liked what it saw, and it became your drug of choice (so to speak). Like if you let a kid eat candy for the first time and introduced them to predominately snickers bars. Snickers is good, it satisfies what the kid is craving, and it just becomes the preferred thing till the next big thing comes around.