It seems that without the catalyst of slavery, and the vitriol towards blacks and the idea that they might obtain equal rights, was probably the only way these issues of states rights would have come to war.
The only thing that really slowed this cycle (which had been accelerating) was nuclear weapons which make outright war between developed nations basically impossible. This beautiful [1] video shows the remarkably frequent shifting or Europe's borders through the centuries. It's easy to just look at that and zone out but you have to consider that each color there was at one time a real and genuine government that the people likely expected to last more or less indefinitely. Many of those blips which you see so seemingly rapidly evaporate were longer lived than the United States. For instance the strikingly visible Ottoman empire lasted for some 600 years. And, in a story told a countless times before and one that will be told a countless number of times in the centuries to come, it wasn't some great force or power that brought it down. It was internal political disagreements which culminated in an armed revolution.
The problem with humanity is that the only thing we want as much as the power to rule ourselves, is the power to rule others.
Eliminating the states' rights aspect entirely leaves you without valuable context when you're looking at modern day political debates and makes it easier to view the entire thing from an absolutist standpoint that simply demonizes the south - everyone in the south was evil because they did this thing that was wrong, but that would clearly never happen to _us_.
Except claims about states' rights are without any historical basis. They were concocted fifty plus years after the fact to cast the Confederates in a noble light. As others here have pointed out, articles of secession specifically call out preservation of the institution of slavery without any assertion of states' rights.