Also, argument of authority: I work for a wallet provider
Also, the code powering each cryptocurencies isn’t immutable. People adopt changes; just not at the same pace as most other pieces of software.
These proof systems are parameterized to ensure a certain soundness error, like 2^-128. So as long as certain cryptographic assumptions hold (in the case of SNARKs, the hardness of knowledge-of-exponent and commitments), it would take an attacker an expected 2^128 brute force attempts to generate an invalid proof. That should remain the same no matter how deep the recursion goes.
Also, though I haven't read the CODA paper either, I think they would only need a single fixed circuit containing a SNARK verifier. Since for a given security level, SNARK sizes and verification steps are constant.