With possible exception of a few immediate decisions, overall, Rommel's "absence" had little to do with Germany's failure at Normandy. Hitler didn't give Rommel the reserved elite Panzer divisions because he was convinced that Normandy was a feint for the real invasion at Calais. Hitler and his gang of Yes-Men talked themselves into believing that since Calais was the most logical location, that any other possibility must be a trick.
The Germans were most effective (Poland, France, Holland, Scandinavia, Africa) when junior officers were allowed to think on their feet, only when Hitler essentially took command did their efficient system grind to a halt. See: Invasion of Russia.
Although the Allied forces had a much heavier bureaucracy (due to "power sharing" - even, at times with that idiot, De Gualle), Eisenhower's strength (most of the time) was letting good commanders take the initiative - and sometimes, unfortunately, not pulling the plug on the bad ones.