I need to try the OP's experiment. I allow the students to use a notecard during the test. So even if they can't quickly memorize something I'm telling them will be on the test, if they are motivated they could write it down.
What's actually more nerve-wracking to me is not students who fail to listen to me, but when I find out just how much some of them do listen to me. I was just grading some essay exams and there were a few where it was like they had memorized my lecture, idiosyncratic examples and all. Of course I appreciate that they are paying attention, but its bothersome that they are just memorizing the examples I come up with rather than thinking for themselves. Bothersome because it means they probably aren't getting the concepts and also because sometimes I'm just grabbing examples out of the air and they might not be the best.
I, too, have this problem.
I was confronted by a student who wanted to know which of the three definitions in her notes for pseudoscience was correct. She didn't know what to do with my response of "All of them. As long as you can write something similar, then you will be ok on the test". She was convinced that there was just one answer that had to be phrased in exactly the right way. Strangely, none of my students feel that way about equations. Any old thing is fine for an equation "because it was obvious what I meant and petty details don't matter", but for anything that involves words only a straight-up memorization makes sense to them.