I'm trying to remember when I had one of those last!
I actually don't love the idea of cheat-sheets but maaaybe if it's a cumulative final I could see it being helpful? If you're taking chapter exams on some material, I think you ought to have worked enough problems so that formulas/constants are drilled into your head. But I guess too, where do you draw the line at engineering appendices? I sure don't have the MoI of every common body memorized.
Well, sure, but, if you don't, then what's the point of punishing you? As a teacher, frankly, I'd be happy to have my students bring in any static resources they wanted to consult—I say 'static' to emphasise not, e.g., consulting a cheating site, although it's fine with me if they've pre-compiled solutions in advance to any problems they think might be interesting or important—except that (1) I think that would encourage bad study habits, and, more importantly, (2) it would be unwieldy in a packed classroom to try to have adjacent people juggling multiple textbooks, notebooks, etc.
In fact, I loved the freedom to give extended-time, fully open-book, open-note exams during the fully remote classes. I wish I could still do that; if cheating weren't so endemic under those conditions, then I would.
To work around the fact that many of us were still in precalc, our teacher just taught us the power rule, the relationship between slopes of tangent lines, etc., without diving into the "why" of why those things worked.
That said, yeah maybe for the most basic of university of physics the whole "derive it on the fly" strategy works, I guess? But when you get to more advanced courses like mechanics of materials, you'll do yourself the favor and take to memorizing at least a few of the commonly used equations.