At 6.117 in Herodotus's Histories, a soldier in battle is struck blind, but claims to have seen a vision of "a huge man-at-arms whose beard covers all his shield." This sounds a lot like the portrait given of Destruction given in the Sandman series: plus, he is in a place of carnage and chaos, his element.

I know that Gaiman has read Herodotus when I was read American Gods. Are there any objections to the notion that he based Destruction in part on this passage?

I wouldn't say that I have an objection,but picturing destruction as a big, bearded soldier seems "natural" enough that it might easily have occurred to Gaiman independently of Herodotus.

Now, if Herodotus' soldier had seen a vision of a sexy, pale young woman wearing tight, black clothes and an ankh, and if he had then proceeded to die, I'd say you were onto something....