There's an obvious safety hazard in taking photographs or video during a pitched battle, particularly in an age where the requisite tools would be very burdensome and require purposeful inclusion in planning.

Taking D-Day as an example, NPR and Fresh Air just broadcasted an interview centered around media, propoganda, and filmmaking during the war. The discussion of D-Day occurs about halfway through the transcript. The tidbit that applies here is that while there was footage taken (which survived the battle), it was difficult for the artists to compile the more graphic footage in a comprehensible or tasteful manner for folks on the homefront, therefore these tapes languished in storage for years afterward.

There are many possible components to impractical coverage - the film can be destroyed during the battle, the government may deem it unairable, or the footage might be unusable. All converge to limit your exposure to the carnage you're asking about. That doesn't mean that there wasn't any coverage - quite the contrary - but a majority of the material is going to be from post-battle or posed situations.

I'd imagine more contemporary wars, with modern pocket-sized cameras may have more of what you're asking about I suppose I don't have to imagine, but to better stick to the rules of the sub (and to avoid trawling through the material too much myself), I'd just ask you to google or search liveleak any recent military action and you'll find a bevy of 'found footage' at your fingertips.