It's Denmark, of course they will turn it in.

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.

It's enthusiasts - hobbyists willing to invest in metal detection gear, spending their free time doing this. If their aim was to get wealthy, they would be doing basically anything else.

Digging for gold artifacts and treasure is not a great strategy to become rich - these people are obviously much more interested in the history, and maybe the recognition. Of course they will turn it in.