In France (a republic, of course) “ownerless property” becomes the property of the local municipal authority (communes), but they have the right to renounce it if it will be onerous. It then passes up to the next tier of local government, (départements), but they too have the right to renounce their rights. It then gets passed to the regional environmental agency, or to the State. So if this situation arose in France, exactly the same thing would happen: it would become an issue for central government because the lower tiers would pass it on.
These “ancient laws”are actually pretty commonly applied in legal system worldwide. In part because there is a public policy objective here to avoid the kind of problem illustrated here: an organised criminal undertaking buys a piece of cheap land using a limited liability company, use it for a criminal enterprise, dissolve the company and walk away entirely secure in the knowledge that the costs of dealing with it would be someone else’s problem.
People who seize on Charles as the baddie here are looking through a very selective lens! This super-dump didn’t appear overnight, for example. How come no action has been taken previously? There was a toxic fire there in July last year - I haven’t seen any headlines asking why nothing happened then (the local MP described it as a “shocking state failure” at the time). And where are the headlines about whoever owns the other 70% of the land who is presumably in exactly the same position as the Duchy?
Clearly there are several angles here if you are looking for a story, depending on what drum you like to beat.