It's worth thinking through the question of whether Iraq or Syria would not be entitled to see stolen property returned due to destabilization. Right now the possessor of the stolen property is an American who also has trafficked in a number of items which were looted in the aftermath of the US invasion of Iraq (this particular tablet was stolen earlier).

Art theft is a real issue in the US and Europe. If an art thief stole then sold a painting owned by an American to someone in China, would you support seeing the stolen property returned to the original owner? Would you take seriously the idea that the owner wasn't entitled to have their stolen property returned since there was a non-trivial chance the art could be stolen again?

For sake of argument, I think that the difference may be that if an artifact is stolen can be recovered. It may even continue to be available to researchers and the general public if it is stollen to be placed in a museum.

It is a much different scenario if an artifact is destroyed either intentionally or unintentionally.

The question of whether a returned article would be destroyed is something to consider, though the notion that this would happen in Iraq and Syria assumes something like another US invasion which caused the destruction and looting in Iraq and Syria the first place. Americans (or others in the Coalition of the Willing) arguing we should keep stolen antiquities because in the future we might destabilize the places we're returning stolen goods to so badly they could be destroyed sounds a little like a threat.

I'm not at all comfortable with the idea that Americans shouldn't return stolen antiquities because America might destabilize the region of the original owner again so badly it could be destroyed.

>It is a much different scenario if an artifact is destroyed either intentionally or unintentionally.

I'd forgotten to respond to this earlier but it's been bugging me, so I'd like to note that a significant amount stolen art is never recovered. In some cases prominent and expensive artworks have been destroyed by the thieves when they couldn't move the art in an attempt to destroy the evidence. Stolen art is sometimes destroyed either intentionally or unintentionally.

Well, one of these artifacts looks to have been in that region of the world for over 5000 years. That's a pretty good track record.

I'm sure the citizens of Philly wouldn't be susceptible to any arguments that Baghdad would be a better place to store the Liberty Bell.

That’s not a very good argument. ISIS has destroyed a lot of artefacts and antique ruins. The track record, even recent, is actually pretty bad.

it was sitting underground and unknown to men for almost all of time

Your first point makes sense but your second just isn't comparable in any way at all seeing as Baghdad is literally one of the most inhospitable places to live at the moment

A good example would be the destruction of Bamiya Budha statues in Afghanistan by the Taliban

but its still theirs. USA or any other nation has no right to take it. Its like China would take the declaration of independence for "safekeeping"