You basically play him for one extra resource, if he sticks more than 1 turn you probably already won, so you're playing him for 1 card and many of the cards are certainly very powerful, but the board clear spell is only 3 damage, the other one can mill you, no way are you going to wipe a full board (which is what is most threatening to a control player). 1 minion is fine, 2 even, but control decks usually already have answers.
He may be great, idk, the RNG is just so damn high with him. You have a 12.5% chance to get the card you really want. He's an 8 mana card that will still take a slot from something else that can be much more consistent. I basically lump 8+ mana cards together, 8, 9, 10 mana... all are late game and you can't have many of them.
I think a deck needs to be built around him slightly, he's not going to fit into a Paladin deck for example. Paladin have too much late game already: Tirion, Primordials, Ragnaros, Spikeridges, DK, Curator, Lay on Hands, N'Zoth... Can't have everything even in that list.
I can see Lich King in Druid for sure, the removal cards can help druid a lot, and they are getting an N'Zoth for taunts, and some taunt synergy cards, so certainly is something to consider. Plus you can ramp to him.
Priest might also slot him because they typically have much less expensive late game (since they use their opponent's late game). And they can summon him out early with that 6 mana card or Barnes, and they can resummon with Servitude, and they are also getting that insane 9 mana taunt. Stonehills in Priest might make sense now.
So yea, he may slot into a couple classes, but it's not an auto-include by any means imo.