@Elganned. possibly, but higher fines might deter and it might pay for increased security coverage for important sites. The biggest pot hunters of the Mimbres pottery in SW New Mecico are the elders of the Morman Church. They have enough money to fight off litigation, plus the present laws are too restrictive for adequate enforcement. Its possible public shame might have deterred the LDS church from of their pot hunting escapades.

@t1nick The UK treasure trove law ensures that the finder is well-rewarded for handing it over and, of course, the average person finding valuable artefacts don't know whether it has any worth, or where to find a contact for the black market in antiquities.
Pilfering artefacts doesn't seem to be a British thing, possibly because most land is privately owned. Even so, the Crown has the legal right to any antiquities that are unearthed. It's just one of those quirks of having a monarchy.
Why doesn't the US government lay claim to treasure in a similar fashion?

@Magister. we have antiquity laws but they only apply on Federal, State, or Municipal lands. Sites in private land are fair game, unless the site is deemed scientifically significant. Enforcement insists that the perpetrators have to be caught in the act with the shovel in their hand and artifact in their possession. We Americans do not value history and antiquity as much as you Europeans. It truly a shame.

@t1nick How can a site be deemed scientifically significant if the aterfacts that would prove this have been sold on? The international ivory ban meant that only antique ivory items could be bought and the seller had prove its provenance before they could sell it. Likewise, buyers could risk seizure of their goods if they weren't able prove it either.
Surely, the US government could find a very easy way of preventing the loss of a precious part of its heritage forever? This is akin the modern day grave robbers of Egypt. It seems a tragedy that capitalism trumps archaelogy when it has so much offer.