While the election of 1800 may have been settled peacefully doesn't mean that sectionalism and nationliat independant sprites within each state were settled.
The debate over the power of the federal government over the state was the question in the 1957 Little Rock Central High School Crisis. and "Federalism" is even being brought up in some of the Presidental Candidates.
That is what the Southern States Rights argument was all about in the mid 1800's. So why didn't that play a part in the Conflict?
No the election of 1800 did not settle the Hamilton-Jefferson forms of government debates by a long shot.