Out of curiosity, have people considered rigidly defining requirements, but rather than picking the simplest/lowest value that satisfies the requirements, instead having a public “parameter choice ceremony” using a multiparty random number generation protocol to pick a random value that satisfies the requirements? That seems like it would make it much harder to manipulate the value by changing the requirements.

This probably leads to regress (why trust the multiparty scheme?), and would only be convincing to a tiny fraction of skeptics (asymptotically, the ones who are least likely to be cranks and therefore the least noisy ones).

Meanwhile, a big part of current cryptographic design is recognizing that many of our current primitives have far larger margins than we really need, and that we can squeeze performance out of our schemes by taking a more evidence-based approach to parameter selection/round counts/etc.[1].

[1]: https://eprint.iacr.org/2019/1492