The efforts to compile good numbers are a difficult task indeed. This is, after all, the first pandemic that hits the country for a long time. Not sure what happens at the interface RKI/Bunderland, but it seems the problem does not start with electronic submission, but from the intelligence generating and patient tracking in the field. While doctors in the 'Gesundheitsaemter' (federal and local public health organisation of the goverment) are on the phone the whole day, tracking and advising people (testing, quarantine protocols) that had contact with Corona patients, the foreign office (Auswaertiges Amt) allows 30000+ people come in from vacation destinations like Egypt without any testing or quarantine, mixing people in planes, and just letting them spread in Germany - effectively sabotaging the the entire process. Moreover, it seems that it is difficult to track infection cascades in high contact places such as hospitals (especially with staff): It is not clear how and when infections are taking place.

As far as I know, they were on the limit of tracking existing cascades in southern Germany last week, and word was that they realized that it was out of hand. Carneval, public gatherings, and failing personal hygiene and isolation, plus our tourists from Tirol and Egypt made tracking measures obsolete. Before that, so my source said, they had a very good overview of the number of infected (minus those without symptoms).