The Nazis played a very destructive role insofar as their rise to power and the treatment of German Jewish intellectuals at universities drove out swathes of highly intelligent brilliant professors and graduate students and forced them into exile (or murdered them). This damage can hardly be exaggerated. There is a famous anecdote that when the local Gauleiter for the city of Göttingen (which featured conceivably the globally most famous German university) asked the head of the university whether the removal of Jews from the faculty had in any way affected daily affairs at the (arguably supreme) Math department, the univerity president was said to have responded blithely "Oh not at all. Because there simply is no Math department left to speak of."

But the Nazi regime in a way was the second doom that befell German academia. The first was the catastrophe of the first World War and the immediate economic disaster hitting German academia afterwards for a protracted decade. Nevertheless German science in particular, especially Chemistry, Archaeology, Physics and Mathematics, still drew international students galore in the 1920s and enjoyed much praise (which was one of the reasons why Einstein still decided to follow the call to Berlin, where he was when he won his Nobel). But despite individual highlights, the 1920s can be considered the moment where German universities began peaking -- the "growth" had moved elsewhere.

The simultaneous rise of American universities especially from the turn of the century (especially Princeton and Harvard; and the similar stellar rise of the modern disciplines at the classic universities of Oxford, Cambridge, Zurich, and the Sorbonne, to name just a few, who had previously been stellar already but now began to draw much larger numbers) had distributed much of the scientific research work away from what one could almost call a German-centric world of science to a more international one, in which English increasingly became the lingua franca of science. This process had already begun earlier, albeit publishing in German and at least being able to read it remained important in many academic fields into the late 1930s (in archaeology it could be argued it still matters quite a bit, but that might be the last one, as today even most German scientists prefer to publish in English to contribute to their field).

One might therefore argue that the rise of English as the modern international language of science would have happened one way or the other as dynamic economies all over the world began setting up industrious centers of research; and English had been more widely spoken globally than German for centuries (obv. due to the British Empire), which makes English today the more likely language for international commerce, research and trade anyway. It only speaks to the enormous global attraction of German science in the 19th century that it had even enjoyed this role of enormous importance between the mid 18th to the early 20th century, just as French had been the language of international diplomacy until the late 19th century (and was still pretty much mandatory for dinner conversations of European ambassadors into the 1950s).