C
So you ask for a COC, one arrives with the goods - Now you find some (or all) of the goods are incorrect.
Can you use the COC in your subsequent claim for damages.
Not a chance !
Can you use the COC in your subsequent claim for damages.
Not a chance !
The additional requirement of certification is akin to swearing in a witness in a court of law. Can they still purger themselves? Sure.
Your point is well taken as to the "real" value of a c of c in terms of reducing the risk of introducing inferior quality processes or components into your product. Most c of c requirements are legal / administrative CYA measures.
The other c of cs that have value IMO are those for special processes where the process is stated, the spec the process was performed to and the key process characteristics are recorded.
These serve the additional function of a "confirmed checklist" of process requirements. Perhaps this falls into your category of those where specifics are "agreed to" as the specifications and processing approvals usually mandate the minum certification requirements.
For example we often subcontract something like stress relieving, cadmium plating, emprittlement relief baking and magnetic particle inspection to a single supplier.
In addition to the results of the MPI testing, a process c of c is required. If the process c of c for example omits the stress relief operation, it could be a typo or it could be that they skipped that operation. In that case we would ask for process records of the stress relief operation and a corrected cert or require that the parts be reprocessed.
It may be the practical benefits all of this is little, but in addition to practicality, most of our customers are what you describe as "ignorant". In highly regulated industries like Aerospace, I don't see the Boeing's and Honeywells of the world changing anytime soon.