Britain and Denmark (at least) have what is to my mind a much better system. They hold that certain classes of archaeological artifacts ("treasure trove" in England) belong to the state. So they require that if you find ancient artifacts you must register them with the government, which will photograph them and note the find spot. If the government deems them of sufficient value that they want them to be public property and go to a museum, they pay the finders the market value of the objects. (Which the finders usually split 50-50 with the property owner.) Hence in those nations most discovered artifacts are reported and photographed and the government has the chance to acquire the important specimens.
After all, much of what we know about Norse myth comes from texts written down in Iceland, in the 1200s AD, most of them by a single man, Snorri Sturluson. How do we know that they truly represent what pagans believed across the Norse world centuries before? There are a few other, older texts, for example Saxo's history of the Danes, but the best confirmation comes from archaeology. There are dozens of carved stones and other artifacts that depict episodes from the myths just the way Snorri described them.
And because of all the metal detecting down over the past 20 years, we now have dozens more such artifacts. Like the Valkyrie at the top of the post, the clearest artistic depiction of a female warrior from the Norse world.
I say, keep hunting, and find more of these wonders.