They survived because most of the aerial bombardment preceding D-day took place in Brittany. This was, after all, to be a surprise attack and the bombardment was supposed to be seen by the Germans as a pre-landing softening of the Atlantic Wall. So the Germans concentrated their defenses in the Pas-De-Calais. As for the naval bombardment, a lot of the troops inside the bunkers were actually casualties of the concussion by near misses as most of the rounds fired were HE rather than AP. That was planned that way.
The Iowa class battleships were not involved in D-day. They were built for speed and range to offer mostly protection to the fast-moving task forces in the Pacific, particularly in their use as extensive platforms for AA batteries. Onshore bombardment was a secondary purpose that could also be fullfilled just as well by even the pre-Pearl Harbor batttleships. HE rounds were more suited to that than armor-piercing rounds. Ditto for fighting against smaller surface vessels.
Battleship AP rounds tended to go right through destroyers before exploding and this allowed Fletcher class screen destroyers from Taffy Force 3 to survive several direct hits form the 18inch guns of the Yamato and the 14inch guns of the Kongo and Haruna while protecting escort carriers (which also survived similar hits) during the Battle of Leyte Gulf, more precisely the battle off Samar, when Admiral Halsey fell for the Japanese lure and went north after a Japanese decoy force of undermanned (basically empty) carriers, leaving the beach front vulnerable to a surface action from the last concentration of Japanese cruisers and battleships while Oldendorff's battle line was finishing another in Suragao Strait. Eventually, though, the destroyer Roberts and the CVE Gambier Bay did sink.
Now I must go sleep.
You Can't Deny It (Lisa Stanfield)