All the way through grad school, allowing a cheat sheet was fairly common. To some extent, I felt like the OP does, but I think it depends on how it is approached. If I’m at work, as a programmer, and I can’t remember a particular syntax or function or I need to work out some formulae, I look it up. What’s important isn’t the memorization of all that stuff, but knowing what I need and how to apply it.
Particularly when it comes to math, there’s two sides to it, one is knowing a formula or algorithm, and the other is knowing how to apply it. A student could have his entire textbook there and the right formula, but if they haven’t learned what it means and how to apply it, it won’t do them that much good.
So, to that end, I appreciate using a cheat sheet. If it was something like what the OP mentions, I’d have no problem writing down a few formulae. Generally, when I did use a cheat sheet, I’d write on it in my normal hand-writing and it would just have a few things on it and, ultimately, I’d rarely use it because, by writing it down and knowing how to derive it, I generally didn’t need to refer to it. OTOH, I remember seeing plenty of people who would bring in a cheat sheet and it would be in very tiny handwriting and covering both sides. I’d often see them refering to it constantly. It’s the latter that really bothers me, because they very well may have step-by-step instructions on everything on the exam.
Another thing to keep in mind, at least as my professors had said a couple of times, is that they tune the difficulty and scoring of the exams based upon what they allow. If it was in class with no sheet and no calculators, they probably wouldn’t require really complex arithmetic and would stick more to concepts. If they allowed calculators, they’re probably have more difficult math involved. If they allowed a reference sheet, they’d probably include a few of the more obscure formulae or be less forgiving in partial credit on incorrectly remembering or applying a formula. And if it was open book or take home, it just got that much harder and that much more harshly graded. So, to that extent, you’re potentially handicapping yourself by not bringing a reference sheet in the same way that if they allow a calculator, and then you’re expected to calculate answers to precision that is unreasonable by hand, at least in the time allotted to the exam.
So, personally, I don’t see why you have to take an all-or-nothing approach to this. Think about what the test is on, decide what parts you feel like are fair to be on a reference sheet, for which I think a series of formulae is perfectly reasonable. Personally, I think having full-out examples of all the different types of problems you might expect to be going too far, and I generally don’t find those very useful anyway, so I wouldn’t include that.