There are situations where they're useful - with questions about emoji for example. It's also technically difficult since emoji are standard Unicode characters and you would have to somehow block specific parts of Unicode and not others.
Disabling then explicitly across the network is undesirable. Disabling them on specific sites might not be technically possible, or at least difficult.
Amusingly, I've only seen serious emoji abuse on petsPets, and I wonder if it's a demographics thing. Considering they might be less technical users - educating them to why they can't use emoji in a post might be neededbetter. A simple block might drive them off.
Edits in rare situations are simple to handle.