I'm genuinely curious how you imagine this system working without a government bureaucracy keeping track of the values of all cargos and regularly inspecting ships to verify the accuracy of their manifests.

What stops ships from reporting something like "Wheat - 25 guilders per ton" when they're actually carrying diamonds?

It doesn't even solve the "It's hard for the bureaucracy to know how much stuff is worth" problem- The government still needs to know enough to decide whether or not to call BS on "Caribbean Grey Ambergris- 300 guilders per pound"

This system does have the advantage that it allows the government to make small fines without the legal burden of establishing that the merchant was lying, but that's in no way the same as self-regulation.

The story is from the 15-1600s. I imagine it working like things generally worked in that time period which is with quite a lot less bureaucracy than today.

The cleverness of the idea is it leverages fear to prevent ships from declaring "wheat" for their ship full of diamonds. You can make some sporadic, random inspections, just enough to keep the fear up, instead of having to inspect every single ship.