Why does this dichotomy fail to prove true in Europe?

London, Paris, Rome -- all are cultural, political, and economic capitols of their respective countries. Why is it that the New World seems to be the only place where this dichotomy occurs?

Because of the shift in economic systems during the same period that the countries of the New World were congealing. Prior to this period, Commerce was controlled from the capitol, usually a capitol that was not created artificially by a nation, but one that grew up over centuries or possibly even millenia. The reached back to a period when the area that controlled the resources was the capitol of a nation because the power could be dispensed from that seat.

With the advent of the nation state and Adam Smith's Free Trade, however, the economic and political componants of the nation became disjoined. As government regulation of trade lightened, merchants were free to move to more commercially viable locations and government centers were free to exist in more defensible or otherwise politically important locations, whereas places having both qualities were previously the best candidates. The existance of a new canvas upon which to build allowed for this to be put into practice -- the old world was already too developed to risk moving much -- the established trade centers served to perpetuate themselves.