Hello Mary Anne, Laurence,
When the Berlin Wall fell, the Stasi files became available to anybody who wished to check them and Katharina Witt discovered to what extend she had been under surveillance. She was utterly amazed. So were many others.
I wonder to what extend the looters were also after files involving their families.
But nevertheless, rampaging libraries, taking all the documentation about their past, not just the recent one but the very ancient one too, reminds us of what happened in Alexandria.

History records involve the long term past and the long term future.
200 years ago, Napoleon went to Egypt with 200 scholars to start a new science: Egyptology that lead to the discovery of Egyptian civilization and Champollion's deciphering of the Rosetta Stone. (I saw it at the British Museum in 1973 during a school trip; I remember staring at it for minutes, noticing the difference of the 3 different writings. We always wore our school uniform with a dark blue tie, gray suit during that trip:).
It's only years later, through Sagan's Cosmos, that the stone's real meaning came through.

We have an understanding of the meanings of such relics of the past.

The looters must have a much more superficial one.

But it's through their own past, their own culture and what it will be able to achieve in attracting the worlds attention (like Egyptology did for Egypt), that Iraq will get a historical meaning.
Those monuments were supposed to last much longer than their oil fields.
Let's hope they have saved the essential.

Raoul