–He’s a Republican. Not only that, but he’s a Republican primary candidate who the rest of the contenders basically hated, mostly for his repeated statements about where the economy was headed (which pretty much were dead on). You’ve got a win-win for the Obama camp: “Across the aisle” with a guy who’s been beaten up by the rest of the Republican establishment. Talking about having your cake and eating it too: Obama would be able to use the terms “Uniter” without becoming a caricature while lobbing a grenade into the middle of the RNC.
–He’s a policy guy, not a banker. This is important because Paul wouldn’t have any “former associates” in the banking industry to cover for, sympathize with, or protect. Paulson, on the other hand, can’t escape the whiff of insider-ism in everything he’s doing. Questions like “Why isn’t the bailout being used as originally planned?” and “Why can’t we get a clear picture of who’s getting the money and who’s being turned down?” may have a reasonable answer, but the overall tone of Cover-Your-Buddy’s-Ass can’t be ignored.
It would make sense, which is why it won’t happen.