The history you describe is internalised only by history-conscious educated people. It doesn't preclude a popularist movement. Also, Germany isn't that unique in having a history of having been in smaller units and having been exposed to lots of wars. (BTW nitpick: the Russo-Turkish wars didn't touch German territory, nor the last Ottoman invasions if we exclude Austria.) Yet separatisms usually produce weaker states.
A lot of moving-around of people existed in the Soviet Union and Yugoslavia, too -- perhabs even more moving around. That is, lots of mixing doesn't necessarily preventing the formation of majorities (or, in an undemocratic context, of a political leadership) willing to push through separation even if it will be painful break of ties for a minority. That's exactly what happened in the Soviet Union and Yugoslavia.
Of course the many Länder are artifical products, but so are the other ones, only older artifical products (what's 'natural' about the conquests of a feudal lord?). But this misses the point. They can gain an identity, or at least a political elite. (Note that the former Central Asian republics of the Soviet Union don't correspond to ethnic borders at all.)
Thus that today, only Bavaria and Saxony have strong local identity, needen't mean much with regards to the future. My scenario for a potential future breakup of Germany would be Bavaria and Saxony going for it, and once they did, similar trends strenghtening in Brandenburg/Berlin and Saarland, and after them in the others, and maybe at one stage some power-intoxicated Landfürsten like Roland Koch decide that they prefer to reign without a federal authority above them even if there is no strong demand from below for autonomy. *Lunatic*, n. One whose delusions are out of fashion.