Er... "active cases"? You probably meant to say "dative" (which is the one case left).

I can't quite draw a definite conclusion on the genitive, though. Maybe they have some statistics. I've never interacted with a German with a different distribution of cases. To me the genitive seems alive and kicking. As a point of comparison, in Dutch in the 19th century the genitive was very similar to German (at least in writing and formal speech), but nowadays it's completely gone and replaced by the "van" construction (equivalent of "von" in German... obviously), apart from a few vestigial expressions. I don't see anything like that in German.

In fact, I sometimes feel that Germans prefer the genitive to the "von" construction that kind of adds unnecessary clutter (admittedly, with one short word).

Well, here you go, another perspective to consider . I could be telling complete nonsense, because as I've mentioned many times, my own command of German is far from perfect. I just know that I can't complain about the lack of genitive. I think the amount I encounter is just right. You mileage may vary.