Crime and theft happen in Denmark as in other countries. But finders get compensated for the metal value so unless they are collectors or have contacts to private collectors, there is not a lot to gain.

I know a guy who found a gold treasure on a field and he was contacted by a private collector after appearing in local news (he turned them down). So who knows how often it happens? But I don’t think finds are common enough that detecting and selling can be a lucrative business. It is usually enthusiasts with an interst in history.