They fit in a certain kind of personal communication, and maybe horrifyingly into some literature, but they don't fit in a lot of places.
I'm ok using emoji with my girlfriend or if I'm trying to be sarcastic or ridiculous, but that's a rather narrow set of my communication. In short it's difficult to show decorum and use emoji. There's nothing wrong with silliness unless you can't do anything else.
We are in a situation where written language use is different and more extensive than days past and it's weakness in English shows. It's difficult to express yourself properly in many situations and while emoji are one way, little cute pictures don't fit the communication gaps.
(the characters are more abstract than most emoji, but only most)