no on Eternal Gems, because you know that some one is going to want to be able to choose the 4 random affixes, and wont be happy until they can be chosen. it is a good idea, but also, something that powerful is going to be hard to get, use, and have a lot of limits. like a .001% drop rate, need 6 to use, can only get them from drops, permanent and unalterable, only 1 per set of gears, not 1 per item like Mythic affixes, and need 6 sockets on the item it is put on to activate.
Edit: and how random are the 4 affixes going to be? Normal? Epic? Legend? Crystal? some combination of all four? and how big a pool will the random affixes be chosen from? the bigger the pool, the harder to get anything you are looking for, the smaller the pool, the less flexibility for any builds you are thinking of making.