I can remember how much focus we put on tense and aspect when learning English: endless lessons on when to use which tense and which aspect (mainly progressive/continuous of course).
There is a term called TMA in linguistics, which stands for tense-modus-aspect as main properties in languages. Now English is certainly strong on TA, while German is weak*. However, I think that German is strong on M, with large verbal complexes a plethora of combination of modals, and, as boaten showed recently, even the possibility to have a modal governing itself, which is just not possible in English. Add in modal particles and it becomes a total mess of subtle differences in meaning conveyed by modality.
On the other hand, we see a lot of recurring questions here about modal constructions, even from foreign speakers which I see as being quite proficient in the language.
I'd expect that students would be drilled on German modal system in a way we're drilled on tense/aspect. Is this actually done or not? Or is it just difficult and even proficient speakers have trouble grasping it thoroughly, much in a way proficient speakers of English keep to get tense/aspect "not quite right"?
*Aspect is that weak that it is not even taught, as many aspect related questions prove.