Considering the horrific human rights abuses the southern whites would've directed against southern blacks had they successfully pulled away, this would be very unpleasant. The only reason the south has treated people who are different decently is because the federal government forced them to in the 1860s and the 1960s, and is now considering doing so with GLBT rights. So from a human rights standpoint, the south needs a higher authority forcing it to obey human and civil rights legislation.
But what if they had successfully seceded? As Paul Krugman has said the rise of the radical right wing can be tied into the growth of conservatism in the south.
Outside of the south, very few states have more than 1 GOP senator. Those that do like Maine or New Hampshire may have moderate GOP senators. There are 17 states with 2 GOP senators, and 9 of them are southern states. Eliminate the 13 southern states, go to a 74 member senate and the ratio becomes 46 democrats to 28 republicans in the senate. Imagine what legislation would be passed with a clear majority in the house, a 62% majority in the senate, and the loss of 141 electoral votes that are almost guaranteed GOP (I'm excluding Florida). If not for the south, the GOP would be a perpetual minority party with no chance in hell of the white house or the senate.
http://en.wikipedia.org/wiki/110th_United_States_Congress#Membershttp://en.wikipedia.org/wiki/Image:110th_US_Congress_Senate2.pngIt isn't that black and white with the house of representatives, but there is still a pattern.
http://en.wikipedia.org/wiki/Image:110th_US_Congress_House_of_Reps.pngAccording to Krugman, if not for the racism of the south, we'd have universal healthcare (the main opposition to this came from southern politicians scared of integrated hospitals and the shift of southern whites to the GOP cut the levels of political power needed to get healthcare reform). Our tax and economic policy would be more like Canada or Europes right now if we lost the south.