Or we could stop asking students trivia and force them to think. Most of my graduate school exams were open book + notes but it hardly helped. You had to demonstrate knowledge by producing a novel solution to the problem most of the time. Not novel as in new research, but novel in the sense you weren't just regurgitating factoids from the books. I also had tons of open book and open note advanced math classes. The problems were made in such a way you had to make a connection with the material and link pieces together in non-obvious ways. In those classes I retained more information even to today.

Teaching, even at the collegiate level, has become "how can I do the least so I can do what I want". Tenured research professors generally make terrible teachers...perhaps we need professional teachers.

For me, the most "open" a test was, the more I worried about it. Expecting students to remember everything on the test meant that it had to be easy.

The hardest exam I ever took was my final exam for Linear Algebra. It was so "open" that people could use matlab on a shared computer that was also projected to the entire class. Turns out, the best students in the class didn't need help on a computer, so it turned into this kind of mind-fuck where you weren't sure if they got a different answer than you because they were wrong, or because you were. To add to the excitement, the questions all tied together and used the answer from the previous one, so if you missed one, you were guaranteed to miss every subsequent question.

This is like any open-book exam. Make the time limit reasonable such that if they know the stuff, they can get it done while referring to a few things in a source, but if they don't know it, there's no way they can look it all up in the available time.