Well for starters, the only thing with an ass fatter than Karn is Kim Kardashian.
Phyrexia is also infinitely more pimp than Jace's eldrazi tentacle porn or Liliana's necrophiliac demon fetish or whatever else the magic writers are trying to pass off as a story these days.
Basically just compare a story like Barrin's to what we get now:
http://www.phyrexia.com/continuity/Barrin.shtml
As for the actual card, in most scenarios, the bare minimum will be that he draws you two cards and gains you 5 life. The other synergy of making a dude for Welder fodder or for offense/defense crewing is very strong as well. I have gotten lucky as well and lived the dream of turn 1 copter into turn 2 karn. I've also had a few games too where he is basically a one man army. We sometimes have trouble closing out matches against the shuffle-Eldrazi decks, be it Omni/Sneak/12-post/etc, and going double -2 gives you at worst two 2/2s, but given our artifact density these will probably be 4/4 or 5/5. He's probably overperformed so far to be honest, but given how well we can protect him, I really don't see how he can be bad. I've been boarding him in whenever I am short on cards i want for a given matchup, since we do run a bunch of dead stuff. I'm only on two copies, but could see the argument for more, although I still think playing the most relevant stuff possible and then filling out with good value things like Karn is the best way to go. It ensures that we are keeping our curve low and not transforming into a bad bridge-stompy deck against decks we aren't adequately prepared to play that role, like ctrl+c/ctrl-v delver or elves.
Whenever we have run planeswalkers historically, it has either been as a solo win condition, or for continued board presence and value. The main ones being:
Koth: his first two abilities weren't really that great, but given the meta at the time, his Death by Mountains ultimate was worth playing him.
Ajani: Mainly for Armageddon in the miracles matchup, but had splash value against creature decks with the helix and the tiniest bit of board control with the +1.
Chandra: Very good card, but more so in a bridge setup since you want to be +1-ing for burn/draw and then to the ultimate and then kill through sensei top tricks.
I could go way more in depth about why each of these could still be good, but don't feel like it. Bottom line is that the double colored mana made it hard to protect with blast backup a lot of the time, and I have really liked Karn's more favorable mana cost and higher loyalty, as it gives him a much better chance of sticking around. All three abilities synergize extremely well with the deck. His card drawing at least puts it into your hand if you aren't casting it vs Chandra's exile, which is important when we are running stuff that we want to cast on our opponents turn like e-tutor or blasts, or even just casting something to fill the yard for lavaman. Chandra might be better than Karn in a deck like mono-red painter, who knows.
Anyways, that's my take. He's just been a 'good' card, which is welcome since we are a deck without brainstorm and we run a lot of horrendously bad cards in a vacuum.
Played my 4th league last night with the 75 I've been writing about recently. They have all been 4-1. Only loss was to Miracles, I made some misplays navigating through a counterbalance, haven't had to deal with that piece of shit in a long time and it showed through my inability to play around it. Other games were against DnT, double RB reanimator, and Aluren. Funnily enough against Aluren I got baited and punished for being greedy responding to a deathrite with double painter and then trying to get my recruiter into canonist. He just responded with a recruiter of his own to win, but having 4 canonists made game 2 and three a breeze. Canonist also at least gives us a chance against reanimator. I powered it out turn 1 twice in the 5 games against it, winning both since it bought me a turn to get painter/blast setup, and limited the griselbrand into infinite discard, ritual into tidespout/iona crap they usually pull. Very impressed with how helpful it was considering how bad of a matchup it is, and has made the cuts down to 1 crypt and 1 RIP in the board passable for the time being.
It's a fun time to be bringing Shortcake back, just want to end with everyone should keep testing shit out as I'm sure there is always a better 75 we can run.