It's not so much the idea of sasuke and karin that interests me it's more of the idea of an uchiha and an uzumaki.
Aaaahhh, and there's the rub. You'd think that it'd be a nice little symbolic thing, a display of unification between Uchiha and Uzumaki, right?
I'll point out the problem with this line of thinking by bringing up an example of another type of one of these symbolic pairings. Faramir and Eowyn from Lord of the Rings (the extended versions of the movies, at least). This nice little pairing was thrown in near the end of Return of the King and it worked in showing how mankind's two most prominent kingdoms (Gondor and Rohan = Faramir and Eowyn) were reunited after years of conflict and mistrust, really giving the message that peace was finally back in the world as Aragorn took the throne of Gondor. This pairing wasn't necessary at all, but it added to the story in a nice way because the characters had no bad blood between them and had us thinking "hey, why not?".
SasuKarin seems to be like that pairing, but it really isn't. Why? Because Sasuke nearly murdered Karin. Faramir and Eowyn worked, to the audience, because we were able to buy it and it only progressed the two characters' development. There was no former relationship-killing (pun intended) conflict between them. SasuKarin. however, would only degrade one of its pairing members. There is an event that happened that got in the way. Now, SK can't just be a nice little add-on like Faramir and Eowyn was. It will only cause damage to the writer's credibility because Karin would be entering a relationship with a psychotic obsessive like Sasuke after he tried to kill her. If she gets with him or even forgives him, then she'll truly just be what we used to think she was: Fangirl Sakura.
If Faramir tried to kill Eowyn while he knew her well and knew full well what he was doing, I'd have raged like crazy. But he didn't. The characters didn't even meet until Return of the King, and even then their personalities seemed to blend well together (therein also lies my problem with SasuHina, but that's another story). This is why SasuKarin can't work as a metaphorical union either. It either asks for too much suspension of disbelief, or just flat out destroys Karin's uniqueness.