> I worry that the more you lower the false positive (accepted to college but uncapable), the greater you raise the false negative (denied college path but capable).
Sure, but if you're trying to avoid false negatives the German system is already poor. In the US work is the goal and there's a lot of talk about finding a job you love. The German system is mainly focused on minimizing the number of people who can't find work. In Germany there's also less of an income gap between professions than in the US (a German doctor or highly paid computer scientist only makes 2x what a tradesperson or retail worker makes https://www.iamexpat.de/career/working-in-germany/salary-pay...).
> My experience, as well as most my peers, was that engineering was about 60% raw mathematics.
Was the mathematics mainly proofs? My US university required a minimum of 2 classes with a significant programming project for a Computer Science degree, and many students took 6 or more courses with significant programming projects. My semester studying abroad in Germany, there was only 1 course offered that even had a serious project component. There was a heavy focus on proofs, and all the hardware architecture courses offered were entirely structured around formal verification of hardware.
