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Not to ask a stupid question, but why didn’t the planners use destroyers to take out the pillboxes with close range direct 5” fire BEFORE the Higgins boats rolled in and dropped ramp? Use those same destroyers to constantly fire suppressive 40mm and 20mm over the heads of the landing troops.
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In Europe, long bombardments were thought to be counterproductive as the thought was it would give more time for the Germans to send armored counterattacks. In the Pacific, where the counterattacks came from the Japanese Navy, they took longer. At Omaha there was only half an hour from sunrise to low tide and H-Hour. There simply wasn't enough time.
Additionally, at Tarawa, in 1943, it was learned that just throwing a whole lot of ammo at a small space wouldn't knock out bunkers. You needed to get in close, aim at the target, fire, then let the dust blow away and fire again after adjusting aim. You could shoot accurately, and get direct hits on bunkers, or rapidly, not both. Again, not enough time at Omaha. To mitigate that, 200 B24s and 300+ tons of bombs were sent in. The fact that it was a 100% miss kinda sucked. By way of comparison, a 5 inch shell on a destroyer weighs 50 pounds. So a lot was riding on the Air Force, which failed horribly at Omaha.
The actual shootout of the destroyers lasted a lot longer then the half hour of the original opening barrage. And shooting from 1000 meters and such was the sort of desperation they wouldn't have considered in the opening barrage.
Also, for reasons having to do with science, the low tide at the British beaches to the east were a little bit later, and they had a few more minutes of naval gunfire prep.