I am sure it is extremely difficult to sort out and identify body parts and remains after severe trauma on the battlefield. Also, think about all the amputations and what happens to those parts of the anatomy. I would assume they are treated as medical waste, incinerated and disposed of. I doubt that many families request the lost arm or leg.
That being said, certainly remains of war dead, even if just pieces, can be better taken care of than to be dumped in a landfill. The military could at the minimum have a site for the ashes in a cemetery, or scatter them at sea or from the air.
Why am I not surprised that anything done by the government is screwed up. Didn't we learn not too long ago that graves at Arlington National Cemetery, our most hallowed ground for servicemen, have been confused and mislabeled.