Not that anyone asked me, but I’d say a national treasure would be something that has historical significance to the country. Now, if it was stolen or ended up there as an act of war, then if it’s ownership can be traced or it occurred during memorable history (such as the nazi looting) then by all means, it should be returned to the rightful owners or their heirs. However, something that has remained (for whatever reason) in a country for thousands of years without a known traceable ownership should remain in that country no matter where it was made.
Aren’t the pyramids and tombs on government lands? If so, then they and their contents should be considered owned by the government and as such any significant find would be a national treasure. I realize back during Carter’s time, there probably wasn’t so much a legal contract detailing the payment for finds, but more of money passing under the table. Now days, I would assume there are such contracts in place to stop the transport of antiquities and hopefully cutting back on kickbacks. Smuggling and other illegals acts is another subject. Antiquities on private lands, imo, belong to the land owner. If the item is up for purchase, the owner should allow the government to purchase it. If the government can’t beat a private collector’s price then too bad, so sad. But again, what do I know.
With the exception of intact tombs (that is, tombs that had not been opened in antiquity - and even Tut's tomb had been opened twice by robbers in antiquity; they simply didn't get much), or works of special historical or archaeological significance, the Antiquities Services and the concessionaire agreed upon an equal split of the treasures.
And while the Giza Pyramids and the tombs in the Valley of the Tombs of the Kings are on government lands, in some countries the state claims ownership of antiquities found on private land. I'd need to do some research on what compensation, if any, is paid to the landowner - the but state confiscates the antiquity.