I meant to skip over PCPs because it would need a separate posts and make the whole longer, I also avoided explicitly mentioning PCPs or SNARKs constructions from PCPs[1] for the same reason.
Yes, concluding about the transparency vs proof-size trade-off is a mistake of my part.
Thanks for taking the time ! will push an update on that bit soon.
[1]: https://eprint.iacr.org/2012/718.pdf