It's not like the confederacy was fighting for slavery and to be part of the union. Both Kentucky and Delaware were happy with the status quo. The confederacy wanted both slavery and to leave the union, which they perceived to be their right.
The federal government at the time was much smaller than the current one and much less empowered.
The union stopped being good enough for them, when it stopped being perfect.
You'd be hard pressed to argue the confederacy wanted to take over the union and then impose slavery on the free states. I mean, you could make the argument, but it's more likely to me they simply wanted to leave and continue enslaving people.
I don't know how this turned into a discussion on slavery. The issue was secession. The civil war answered that us states cannot secede. Itll be interesting to see how the dynamic in the eu changes since this is a possibility there (although I'm doubtful they'd let a continental member leave).
I can't see its use being refused: that would disintegrate the bloc. And there was no question that we (the Brits) wouldn't be allowed to, so the precedent has been set.
I would imagine a few tweaks to the Article 50 exit mechanism will be made next time the treaties are revised - there are some game theory problems in the current trigger mechanism and the timescales set down turned out to be too short in practice - but it's no longer in dispute on principle.