Exactly, I strongly believe that any test at a secondary education level should be open book. We should be testing for reasoning and capacity to apply knowledge not rote-learning.

It's also why I believe that in most cases multiple choice questions have no place in any well designed tests because it's extremely hard to create multiple choice questions that actually test the application of knowledge versus the regurgitation of rote learning.

When I was in university (grande école) in France, luckily all tests followed that format, they were open book, very few questions that needed deep detailed answers and were about interesting problems. Even finding tests from previous years and doing them was actually fun (tests were never reused).

I did an exchange in the US at RIT and most tests had very boring rote learning questions. For example in a computer graphics class: Which company were voting members of the OpenGL Architecture Review Board? Which year was the first OpenGl specification released?. I still remember those questions because I was shocked by how utterly stupid it was to have those on a test but, in general, 25 to 50% of the points of any tests was on those completely irrelevant, useless questions that anyone can google for.

Cheating is a problem for universities that never had proper testing standards. But that's a symptom of incompetence on the part of professors and of universities not making the choice to ensure that tests have to be well designed.