The same reason is given at Newgrange and Knowth. Flash photography could degrade pigments, but there's none at either site these days ... They quote respect for the 'Sacred Place' and the yanks go "Oooooh"*

The real reason is that they want all the royalty monies for images :-)

With smaller sites with little visitor traffic I fully appreciate this as being necessary to keep the site maintained, but with Newgrange and Knowth? I think not.

* Not <i>all</i> of them do this, just a few.