The important variable is the staff/student ratio, not the size of the country. With few students per class, or many teachers, this scales fine. I'm running similar exams for my (UK) Masters modules, but colleagues are reluctant to do it for the enormous compulsory survey courses as there are several hundred students in them (vs up to about 50 in the MA ones).

For a large compulsory survey course, a well written multiple choice test should suffice. If the test is well constructed, teaching to the test should cover exactly the required material and be no impediment.