If the US were broken up into smaller units, though, it wouldn't necessarily have followed that the South would be more "conservative" in the way that we think of the word today. Parts of the South might well have become another Haiti or Brazil or South Africa, either repressive or anarchic or both. Or they might have followed demagogic leaders into more radical statist or egalitarian forms. Or settled down into a political system not so different than we have now.
I suppose the South and the West do keep the rest of the country from following Canadian or European political patterns and models. But if we broke up the country today, all parts would sooner or later gravitate towards those foreign models, or else adopt truly bizarre political systems. In today's world, markets and media tend to push countries in similar directions. Should we give way to disunion, European ideas would become more potent with out the example of a strong united American union, and eventually those ideas would prevail.
It would not be a question of how much more Canadian America would have become, but how much more American Canada would have become.
OTOH, one wonders how much of Mexico the southerners would have managed to aquire on their own, or if Bonaparte would have sold his Louisiana territory to a weaker [southern] neighbor.
Given the martial nature of the caveliers, I could also see them getting into a war with Spain over Cuba, or France over New Orleans.