> From the point of view of an 18th- or 19th-century person, for whom the purpose of the mint was to certify the value of the precious metal in the coin by stamping it

Was that the purpose of the mint? That would imply that the relative value of silver vs. copper was static.

It was, yes. The varying relative values of metals was in fact a huge problem for mints for many centuries. The problem was sometimes resolved by refusing to mint any but the priciest metal, and at other times by the values of different coins such as shillings and sovereigns varying relative to one another.