While I can’t speak much for the American experience, I can certainly offer some particulars of SHAEF (Supreme Headquarters of the Allied Expeditionary Force—basically the overall coordinators for the Allies) planning that influenced this.

For one, we should note that the timing for launching the amphibious invasion was still very early morning, with quite limited light available, in order to have surprise. However, the landing craft were not actually the first part of the invasion. During the night, minesweeper crews worked feverishly to remove as many obstacles as possible without alerting German forces. C. P. Stacey, the official historian of the Canadian army, cited these efforts as potentially saving hundreds of lives, as landing craft were much less likely to hit a mine and be lost with all hands. That brings me to my next point: landing craft moving in the darkest part of the night would be at a severe disadvantage. The beaches (and particularly Omaha) were fortified. There were mines, Czech hedgehogs (the big spiky things meant to prevent tank landings), German bunkers, and natural obstacles such as rocks and reefs. While moving under the darkness would have extended the element of surprise, it is extremely unlikely Allied troops would have been able to clear all German defences before the Germans noticed. In that case, all the Germans have to do is sweep the beach with machine gun fire. While it is theoretically possible to still take the beaches under this scenario, it relied on a heavy element of luck to extend the element of surprise, and did not promise more secure results than moving in the pre-dawn light which allowed the Allies enough light to see. After the disaster at Dieppe in 1942, much had been discussed in SHAEF command about avoiding relying on luck as a part of a successful plan. This has been cited by several historians (Stacey, Keegan, Zuelkhe, and others) as a strong argument against a full night time invasion.

Further, while the airborne and seaborne invasion had the same ultimate goal, i.e. securing a foothold in continental Europe, they had very different goals. The airborne invasion was to help ensure the land invasion, by blowing bridges and key communications towers to prevent aid from getting to the beaches. If that were to be happening concurrently to the sea invasion, bridges and radio towers may still have been standing, which defeats the purpose of the airborne invasion in the first place. The actual effectiveness of the airborne invasion is sometimes debated—many planes dropped troops in the wrong areas, resulting in a truly unfortunate rate of loss amongst paratroopers who drowned in swampy areas, or who dropped too close to German troops and were shot down or taken prisoner. The fact remains though that SHAEF’s goal for the airborne invasion was to assist the much larger amphibious invasion, rather than act as a true separate invasion force.

While we cannot speculate on the outcome had the invasions been launched concurrently, there is a significant body of evidence to show that SHAEF examined all possible invasion plans (remember, planning began in 1942 for the 1944 invasion) and concluded that a separate air and land invasion with different goals was most likely to be successful, based on all available evidence and experience that Allied armies had up to that time.