They're definitely still being used today, though in my experience, we weren't docked points for syntax errors where the intent was obvious, except in the introductory classes where the syntax was one of the criteria being tested. In the algorithms and math programming courses, legible pseudo-code was often considered fine.

Pen and paper definitely make it easier for the test administrators to prevent cheating with resources saved on the computer or using the internet. In one of the introductory engineering programming courses, which was electronically submitted in class and auto-graded, there was an issue one semester with students using TeamViewer during class and having others take the test for them.