The main reason for the corpses not being able to stay permanently is the potential number of them on screen at one time, and specifically that each corpse is affected by physics, allowing them to be blasted and thrown all over the place by the force of player abilities.
It's one of the trade offs when integrating new technology, you can get really awesome effects, but they do have a cost. In a 2D world, a sprite of a dead creature doesn't really cost any more (system requirement-wise) than a sprite of something that's alive. Probably less. In a 3D world where a creature dies and then needs to have physics calculations thrown onto it so it can bounce and fall and fly around, they cost substantially more.
We remember fondly those situations where you've just completely obliterated a camp of Fallen, and as you're picking up items - marvel in your destruction. That's a feeling and part of the gameplay where if we can realistically keep some of it without sacrificing features or having insane system requirements we'd definitely like to, but no promises.
When questioned as to how skills like Find Item, Corpse Explosion and Summon Skeleton would work in D3, if they were indeed included, he responded:
We haven't announced any abilities outside of those listed on the website, so by discussing what is or isn't in the game I would be essentially making an announcement, which I'm not prepared to do.
Thanks for the tip, Dead9k!