I have also memorised the formulas for d/s/t and f/a/p but struggle to see how these translate in to academic excellence of any type, or even why giving them to someone is encouraging mediocrity.
There is (imho) nothing of value in memorizing simple formulas, and everything in the value of knowing how and when to apply those formulas, or where to Google for them.
The presumption that students have memorised the formulae allows you to build more complex tests with confidence that they will tease out understanding and not just computation.
In my highschool physics exam, about 2/3rds was of questions based on memorised formulae. For example, the bouncing ball problem, with a series of questions to tease out our application of calculus, memorisation of compression rules and so on.
Then comes the final question. I remember it well because at first, I did not know which formula to apply. Water wells into a pool at rate X per hour, falls over a waterfall into a second pool below, which drains at rate Y per hour. When it falls over the edge of the waterfall, the water is at temperature A; at the start of the problem the temperature in the bottom pool is C.
After an hour, what will the temperature in the second pool be?
To solve this problem you actually need to consider the thermic effect of water falling. You need to build a single equation to accounts for acceleration due to gravity and the beginning temperatures of each pool. Then you need some calculus to transform it into an equation that will spit out the final numerical answer.
The only reason I was able to attempt and solve this problem was because I had memorised the equations. There simply would not have been enough time to try to reverse-engineer a bunch of anonymous letters in-flight.
Similarly, when I studied law, all exams were open-book. This is because, as a law professor told me, "it lets us ask harder questions". There's simply no way to synthesise thousands of pages of material in an exam setting. Either you learnt it beforehand, including a whole bunch of flat out memorisation of details of cases, or you didn't. Having your casebooks for reference is useful, but only to check a detail or reuse a quote.
I'm no physicist, but even if the typical physicist has internalized tons of relationships expressed in formulas, students who have a cheat sheet of tons of formulas still have to frame the problem and then choose the right relationships to solve it, and hence they learn and grow the way we want them to. Maybe I'm wrong, but as a software developer, memorizing syntax speeds me up a little, but when it comes to the entire development lifecycle, the quality and length of time will depend much more on whether I framed the problem correctly and used the right relationships than whether I quickly recalled syntax. It's not totally apples to apples, but it seems like in the 21st century we can get so much more done if we focus on knowing where to look up information and have learned how to use it, much like how I look up APIs and design patterns as a routine part of my job and don't think it really slows me down to have to do that.
This is a slight tangent because it is about mechanical computational skills rather than formulas, but the idea is the same.
I am currently teaching a bunch of very bright graduate students from a number of countries. On the most recent midterm, students from countries that force people to learn to compute and learn some formulas finished in an hour, while US students and some others took two. US students in particular were caught up on figuring out the solution to x+y+z=1, x=y+z, y=4z. Just impossible.
US students in my class are wasting time on mechanical calculations rather than understanding the meanings of the theorems they illustrate, because they have weak computational skills. I can't write problems that are computationally easy enough. They are unable to apply their much-vaunted "creativity" and "critical thinking" because even once they Google a formula they can't carry out meaningful work with it.
I can Google how to use a hammer and a table saw, but I'll produce a crappier table than the person who has so much practice she can use them without thinking. That person can think about the final design while I think about not hitting my thumb or slicing off a digit. The argument about knowing how and when to apply formulas misses the fact that practice in applying those formulas is essential to competence.
There is (imho) nothing of value in memorizing simple formulas, and everything in the value of knowing how and when to apply those formulas, or where to Google for them.