Is this really the case, or is it just chance that a few major examples you're aware of are this way? Could any historians shed some light on whether this phenomenon actually exists?

Brazil is like that too, but the south/north logic is inverted.

I'd recommend crossposting this question to /r/asksocialscience.

Germany was divided by East and West, although those were outside forces.

Edit: Eastern and Western Roman Empires. Just saying.

The Chinese wheat growers verse rice growers divides has been used to explain the cultural differences in the country there. The rice growing south, where production requires a more community based approach, has a much more communal and holistic identity that we often associate with East Asian and Chinese culture while the northern wheat growing regions have a more individualistic streak associated with Western culture. Hears a study that supports these results http://www.sciencemag.org/content/344/6184/603 . Of course that's only one country with a unique scenario but it offers some insight into at least one reason one country does.

Climate is one of the major reasons for socio-economical North-South federalisation within larger European countries (among others).

Much of the economic divide in Italy, for instance, has to do with industrialisation and urbanisation in 18th-19th centuries. South Italy, with warmer mediterranean climate, and rare snowfalls (Rome, Naples, Abruzzi, Palermo, etc.) was rich and agriculture-oriented since the Antiquity - compared with the cooler Italian north. During the industrial revolution; however, the agricultural sector of the developed European economies has shrunk, giving way for industrial production in the urban environment. As a result, starting in 1890s, southern Italy saw en masse emigration to the industrialised cities in the North - land tenants and farmers left for promise of greater personal wealth in the cities, profit security as wage-workers, etc. etc. The reasons were similar to those of mass urbanisation in most late 19th century industrialised countries.

From this follows a conjecture that the rich agricultural regions of Antiquity/early Middle Ages (South Spain, South Italy, the Fertile Crescent, etc.) were ill-prepared for the socioeconomic changes of the late 19th century. In the cooler Northern regions of many geopolitical entities, the lack of reliance on agricultural produce has led the resident entrepreneurs/princes to pursue maritime trade and city-based production as a source of income/sustenance. In the age of exploration, maritime exploration has opened up new opportunities for maritime trade, richening the merchant republics of the North Italy. Industrial revolution bolstered the inland cities (such as Milan, and Lombardy in general) because their economy had to take up industrialisation as a viable alternative to meagre agricultural produce and lack of access to the coast (hence reducing trade opportunities). Basically, with the semi-autonomous and often independent Italian states pursuing different economic strategies, each would invest according to their climate and geographical conditions. The scientific/industrial revolution has then favoured those which industrialised quicker (just as age of exploration favoured coast-based trade republics).

So why didn't the rich agricultural regions of South Italy industrialise/develop faster, making use of their superior wealth in the Antiquity and the early Middle Ages? The simplest answer is that they didn't have to until it was too late. Reliance on agricultural produce crated little need to pursue maritime trade/industrialisation - and also political strengthening the feudal/land-owning class that was far richer (to begin with) than in the North. More difficult climate/geographical conditions for the medieval princes of North Italy meant that they were willing to give up more power to the bourgeoisie merchant class and later the industrial producers - in turn increasing democratisation of these areas.

Of course, this analysis neglects to mention the poltiical landscape of Italy (among other countries) and its effects on the North-South divide, but I thought I'd concentrate on how climate helped shaped economy and politics.

Thanks for the interesting question!

Though I'm not sure your premise is actually true, assuming it is there is a possible explanation: climatic zones. Different areas of a country may have (often North/south) differences in which crops can be grown and in what quantities, leading to regional (perhaps north/south) differences in the tendency to industrialize/modernize. Due to latitudinal differences these climatic zones might vary most strongly between North and South.

One very big example that you may enjoy is Rice Theory which posits that whereas wheat-growing cultures like northern China can be individualist and self-reliant, rice-growing cultures (like the rest of east Asia) require community efforts to farm rice, resulting in stronger communitarianism.