> The first exam type tests what you are expected to have learned. [...] Each problem must therefore have a small solution that is easy to find without any special insights. That requirement alone limits the applicability of such exams to confirming that the student has a sufficient understanding of the topic to continue to more advanced topics.

This untrue implication. You can have difficult exercises that do require special insights with long solutions and still keep it within curriculum or "what you was expected to learn". What you cant do is to give them exercises that require one more chapter or invention of difficult to prove theorems that were not taught.