Overlord, German best case

So I have been pondering this for a while. What would the likely outcome be if the Germans managed to get it right during Overlord

So, assuming same day, same weather etc

Rommel doesn't go home on leave
Hitler's sleeping habits somehow don't affect the German response times
(Feel free to add extras)

Presumably the basic German move is to rush their armoured units towards the beaches immediately, but what would this achieve?

Allied air cover still means that such movements will be slowed, and there will be a toll on the fighting strength of these units - the historical journey of Das Reich is a good model.

Typically German armoured attacks on Allued positions in Normandy were repulsed with unpleasant losses (the 6pdr / 57mm AT gun was very capable)

If the Germans manage a real best case, and reach the coastal zone before the allies are off the beach and properly consolidated... then they get obliterated by naval gunfire in addition to tactical bombing

I'm open to being proved wrong, but as far as I can work out, if the Germans had a better response on DDay then yes the landings would have been harder, but the Germans would have had a lot less armour around to defend Caen.

 

Ike gambled. What if the storm stopped the landings? The troops would drown without a German shot fired? It was a chance he took.

 

There was no operational plan the Germans could have executed that would have overcome the overwhelming Anglo-America air superiority over Normandy.
The reason, of course, that Rommel wanted his heaviest forces at the coast was because Rommel knew, from experience in North Africa, that he who has air superiority dictates all movement.
But even if Rommel had completely gotten his way, the Anglo-American air superiority would still have annihilated Rommel's forces in the open.
If one reads German accounts of being in Normandy, everyone said "where is the Luftwaffe".
This is exactly what one reads in French account of May 1940, "where is our air force".