im with carl on this one. Emotions can be shown, very well aswell. But its the animators instead of actors that prvide it (combined with the director in both cases). CGI the combo, even though i feel its really closer to animation than actors, even when u use motion capure. Look at Golum, good example, the Hulk aswell.
And regualar paintings, well done and u can for sure see emotions of those painted.

But i know that anime and cartoons is not for everyone, so i think its more that which is the problem, not the lack of ability to show emotion. Some ppl just don't like animated stuff.