Parameters generated this way are called "nothing up your sleeve" numbers.
Yesterday I texted my coworker a suggestion to dockerize his yocto build so that it would work better in vagrant on a lambda server in the cloud. It's borderline these days, but he realized I was being facetious. He retorted with a serious comment about 500 lines of typescript to run 5 lines of bash.
This generally narrows down the options to something were relatively little trickery is possible: keep in mind that the eg. hashes used to break some encryption would have to be very specific so that the algorithm isn't trivially broken to begin with.
The more important part about nothing-up-my-sleeve is really the justification for choosing a particular hash/number. If, let's say your algorithm needs a prime with at least 10 digits and you pick the first prime with 10 digits nobody asks questions. If you picked the 16th, then people would ask questions.
Similarly, if you can pick any arbitrary ten digit number and you pick the first 10 digits of pi, nobody will ask questions. If you picked the million'th to million-and-tenth digit of pi people would asks questions.
"meaningful" has to be understood more as "from a pool of constants that leave little room for (mallicious) adjustment". The abstracter the number, the higher the potentially used searchspace.
"aes" is better than "aes is the best!" which is better than "aes123884586314745"
From "SEC 2: Recommended Elliptic Curve Domain Parameters":
"... one type being parameters associated with a Koblitz curve and the other type being parameters chosen verifiably at random"
"Verifiably random parameters offer some additional conservative features. These parameters are chosen from a seed using SHA-1 as specified in ANSI X9.62 [X9.62]. This process ensures that the parameters cannot be predetermined."