Completing my trinity of stream-relevant Dominaria cards, I think @Prospero and @Protoaddct have added pretty good insight here. First, I agree with Nick when he says he doesn't see this card being playing in Shops. It's just too hard to reliably cast the card through Sphere effects when you can't count on Mishra's Workshop to help you. If it was an Artifact, the card becomes pretty absurd in Shops, but I guess WotC didn't want the marquee Planeswalker in the set getting killed by Abrade. That's actually good news for Blue pilots as it means Null Rod doesn't shut Karn down and Dack doesn't steal him.
@Protoaddct has identified the most relevant ability on the card - the -2 ability is where the money is at. Once you deviate from cards like JTMS, JVP, and Dack, what you are looking for isn't typically a draw engine but a win condition. Chandra in the various decks that have run her hasn't been there for the card advantage or the creature removal. Now, she can be used for that and that's part of her utility, but for the most part I want to -7 her asap and win the game while the opponent struggles to answer her. Similarly, Karn as a card advantage engine is somewhat anemic. Someone previously summarized this but the +1 ability is worth less than a random card from your deck since you are getting the worst of the top 2 cards. The -1 is worth more than a card as you get to chose from the best of multiple cards. The net advantage is 1 card a turn unless you have some sort of deck manipulation to extract value from digging two cards deeper each activation. Again, not bad but JTMS provides that +1 raw card advantage and increases the quality of cards in your hand. This happens immediate where Karn has a delay, meaning a JTMS topdeck is very likely to win you the top deck war, where card provides a pretty significant window still for your opponent to draw some of those broken Vintage cards and end the game.
Now there are certainly ways to extracting more value from Karn - Dack can address the card quality issue through the card selection he provides. I think it is better though to aim to maximize Karn's strengths. It's pretty clear that the power of the -2 is contingent on the number of artifacts that are in your deck. What power and toughness would you expect on a creature for 7 colorless mana? A 7/7 with downside like Traxos? Juggernaut? What about when you get to add a second copy the next turn? In my games on stream, Karn was typically making 6/6 or 7/7 constructs. Which is well above the curve when you consider the fact that you still have a Karn in play that the opponent has to deal with or face a stream of constructs or card draw. Granted this is a deck that is running a ton of artifacts (Seat of the Synod, Mox Opal), but why would you want to run a card in a deck that doesn't make full use of its abilities? Oh, and I've tweaked that deck a bit. Is 4 mana for a 20/20 good?
The deck above was running 1 Karn in a The Antiquities War/Paradoxical Outcome deck. I'm still feeling out both those cards, but I will say that the added dimension of attack is very powerful. Karn and TAW function as win conditions that work independent of PO (unlike Tendrils) and are compact in that you don't have to run cards like Voltaic Key and Blightsteel to make them work (improving on consistency, which is a major issue with PO decks). Opponent plays Kambal or Damping Sphere, make artifact creatures and beat down. Don't draw artifacts or PO, make artifact creatures and beat down. The advantage of Karn in this context is that he works well within the actual PO loop as you play him, make a creature, pick him up with PO, and then repeat until you find Time Walk and attack for 80. In many ways, Karn is more akin to Monastery Mentor in the PO deck. And that certainly deserves exploration going forward.