The problem are that you compare northern Germany and the Nordic countries with wrong part of Europe, when they really should be compared to Poland. 17-18th century Poland are how Catholic north Germany and the Nordic Countries would have looked. Lutheranism focus on literacy ensured that the Lurheran countries had the highest literacy in 17-19th century Europe, entering the clergy changed from a way to get rid of surplus children and became a way of social advancement for a family, often the children of priest would become lawyers, which while a sideway step, created the large academic classes of Lutheran Europe. This was not effect the princes planned but purely accidental results of Luthers theology.
That's not a fair comparison. Economics had already led Poland and Germany to split from one another socially. Already, in the early 16th century, the foundations in Poland had been laid for the Golden Liberties and the plantation-like grain economy, neither of which were present in Germany in anything like their PLC form. German burghers constituted a huge part of the urban Polish population long before the Reformation--urbanization, and with it literacy, were much more advanced even in pre-Lutheran Germany than in Poland. Mostly, this was due to Poland coming to the urbanization game late and due to its governing caste (the
szlachta) holding urban life in utter contempt (also, to the alliance of the Polish aristocracy with the Jews and Armenians, whose domination of the Polish civic economy stifled the development of the Polish burghers).
There were already large academic classes in Catholic Europe, even in Poland, whose aristocratic and burgher families sent their sons to study in Italian universities and whose kings founded domestic universities. The abolition of clerical celibacy in the Protestant countries did not have much impact on this, though the widespread literacy probably did help. But then, what came first, the literacy or the heresy? A large class of burghers and a peasant class not tied to the land in a state of near-chattel slavery is already going to be more literate than its neighbors in Poland, which makes them more likely to read Lutheran propaganda.
I say the proper comparison is not with Poland (which, IMO, has more in common with Hapsburg Spain than with Lower Germany, in that both had a cultural complex about being a bulwark against the infidel, which led to the propagation of a large class of impoverished aristocracy, and rose to the peak of their strengths riding an ultimately transient source of income that they failed to leverage into real economic development) but with Flanders or northern Italy, whose urbanization and civic cultures were a better prototype for those northern German, Baltic, and English merchants who would come to dominate Europe. And mass literacy was already manifesting in those areas over a century before Luther--by 1339, half of Florence's children were learning to read. In Flanders, an organization called the "Brethren of Common Life" were preaching the importance of literacy and reading religious texts as early as the fourteenth century. Town schools, staffed by priests but secularly-focused, were present in Flanders from that time as well.
As much as Luther has been credited with accidentally inducing mass literacy in northern Europe, I would argue that he would not have been nearly so successful were he not preaching to a literate audience (consider, as a related example, the decline and eventual demise of the Polish Arians in the seventeenth century, compared to the persistence of Polish Lutherans and Calvinists in the much richer, more urbanized areas in Prussia and Livonia).
Without Luther, northern Germany and England and possibly Sweden would probably have been just as literate as IOTL--the movement toward that had already begun, and seemed to be more tied to urbanization and trade than to theology. Of course, that just makes them fertile ground for some other rabble-rouser calling for the destruction of the icons and the priest's beheading.