That wouldn't be practical. It would make fonts too big, and videos aren't a thing that goes inline in text.
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.
I mean, this ship has long sailed, but that was a mistake nevertheless. Not everything has to be a unicode character.