I would argue (as a native speaker) that "wegen den Regen" is also possible and basically is equivalent to "wegen den Regenfällen".
Of course I am biased but I actually believe that there is no other language that is so elegantly conducive to precise thinking. And above confusing example is actually illustrating this. If thinking is a bit like moving around on a high-dimensional mental manifold then language is an imperfect projection onto a mostly serialized data structure but with referencing (maybe 1.x dimensional). (If you project something from n dimensions onto less than n dimensions you always lose information)
And with German you can explore this mental manifold in a depth and strictness like with no other language. Like entering a meta debug mode where you can form a sentence creating an implicit reprojection into the space where the manifold resides and then muse about how this makes sense.
I often find myself doing that and playing around with "understanding" a sentence in different ways. A simple example would be that you can take almost any German sentence and by stressing a different word the meaning subtly changes. An analogy could be those pictures where you see something and after looking long enough at it it looks different. For example a sketch of a 3D box which you can flip. At some point you can do this intentionally by applying an invisible switch. Same feeling with German statements.
But German has also some short comings especially in the emotional department. For example there are no good translations for "smile" and "to look forward to". Another language I dabbled in is Thai which is pretty much the total opposite of German - very fascinating and refreshing.