A constrained parse dialect could be a parser generator, and the constrained dialect could probably subset the unconstrained one pretty closely.
But unconstrained PARSE as-we've-known-it is quite dynamic. I've tried to nail down some minimal rules for the sake of coherence:
When Should PARSE Notice Changes
My main point of view that where this fits in the "Loom of Language" is packaging this kind of methodology in a way that brings it to the common programmer, using naught but mostly-C89. A kind of "organic, locally-sourced software" without inscrutable additives and preservatives. I want it to be constructed obviously and my performance goals are modest--seeing it as a toy almost more than anything.
This is in contrast to fairly bold claims about the pervasive applicability of the medium, believed by Carl and Red.
Ultimately if it gets used by others, it won't be up to me. I don't know if you read Graydon Hoare's bit on Rust going in a direction he didn't envision--but that his vision probably had no realistic future:
https://graydon2.dreamwidth.org/307291.html
Maybe my more humble framing isn't the way the world will take it. I don't know, but I'm glad you see potential in it!