Trouble was, the Allied naval (and air) bombardment was anything but accurate on D-Day. My understanding is that the most successful bombardments were provided by the smaller ships (like destroyers) that ran right up to the beach (risking grounding) and thus could directly see their targets. Smoke certainly would have disrupted that support, but it would haven’t meant anything to the larger, indirectly-fired guns that didn’t have as much of an impact on the beaches themselves-- seeing as they were relatively ineffective even with spotting, not firing at all (or being relegated to pre-sited targets inland) would have made little difference.
That said, no one in the Allied High Command would have voluntarily ceded what was, on paper at least, one of their greatest advantages over the German defenders: their overwhelming fire superiority at the point of attack.
Eh, I think the difference in military effectiveness between [the German defenders everywhere else] and [the 352nd defending at Omaha] is the predominant factor in the casualty difference, not other details.
Add to all of that the fact that Allied intelligence was unaware that the 352nd had moved up to the beach, they thought it was still located at St. Lo:
There’s never been any controversy over relative performance on the beaches that I’m aware of. Utah was a pushover, with little resistance, Omaha was a bloodbath because the landing was made into the lap of a high quality division that the Allies didn’t even know was there, and the landings at Gold, Juno and Sword fell in-between, but also were counter attacked by the 21st and 12th SS Panzer Divisions later in the day.
Regarding the use of smoke, consider how far landing craft landed their troops from their designated beaches on D-Day as it was. Now factor in massive amounts of smoke. And as Little Nemo notes, the effect of the smoke on the Germans wouldn’t be very great. The Germans didn’t really have to aim; the entire beach had been pre-registered by artillery, and machine guns had designated and interlocking fields of fire set up. All they had to do was shoot in pre-established lanes of fire, and smoke or not they were going to be hitting the troops landing and on the beach.
