So a peach emoji is not the same thing as the iOS peach-emoji-image. Similar to how changing my font doesn't change the actual characters.
I don't think including emojis was a great idea, but now that it's happened and people everywhere use them, emoji have become characters. I agree with your point, but it's already happened and so now there's not really any going back.
I mean, this ship has long sailed, but that was a mistake nevertheless. Not everything has to be a unicode character.
For example I could see there being an emoji for keyboard cat.
However, I could totally see some kind of open source GIF library of a few hundred meme videos and pictures, to standardize the "Reply with a GIF" thing in some P2P chat ecosystem, and maybe it could have a new URL scheme for referring to OpenMemes images.