I can't stand the animation in anything in the last......at least ten years. Especially Justice League and anything like that. Somewhere in the late 90s, they started drawing people unlike people. Some of the last great animation were Ghost in the Shell, and Mononoke Hime.
Blame John Kricfalusi.
Blame budget restraints. Cartoons have to be drawn simplier to reduce costs. This is why shows in the "Bruce Timmverse" like Batman started out very traditional and evolved into this very angular style by the time Justice League came out. Straight lines are cheaper to animate. Anime style is also cheaper to animate, again for the same reasons.
That being said, with the exception of feature films, I can't remember any time in which people were drawn realistically in cartoons. Before you start talking about shows like gi-joe, the old thundercats, ect... so back and watch those. Yeah it was a more realistic style, but the quality was horrible, almost unwatchable by today's standards. They looked that bad, again, because of budget restaints. In the mid to late 90's animators figured out that if they drew their characters simplier, that there would be less mistakes. Even if you go back and look at the first couple of seasons of Batman, when it was drawn more traditionally, you'll find tons of animation errors and glitches. In subsequent seasons the characters were simplified and the errors disappeared.
So it's a balance really. Also Avatar, The legend of Kora, Black Dynamite, The Boondocks, Archer, and Metalocalypse would like to have a word with you. And that's just the ones I can think of off the top of my head.
