Writing code on paper was a practice I initially resented when taking CS courses at University. However, it made me a better programmer, because it forced me to think about design and data structures first, then about the code.

Let me be clear: I think it's a great way to test students as long as the graders/instructors aren't overly anal about syntax or even API correctness. I was lucky to have teachers who were okay with unbalanced parentheses, made-up API functions, and in upper-division classes, pseudo code was even acceptable (data structures). (However most CS classes will be biased towards imperative programming over functional programming).

To use a cooking analogy, if you have to think about how you are cutting the fish, you won't be able to think about how you are going to prepare or cook the fish. Writing code on paper forced me to think about design first; that is, it enabled me to think about what I was going to do with the fish.

Meh. Writing code in pencil was annoying, but I was perfectly well able to finish all the exam questions in the allotted time, despite having the world's worst handwriting, and not having actually taken the course.

Imagine how much worse it was when it was in C++! ;)