There were a couple of reasons for the lack of close air support; First, anti-aircraft fire and weather conditions (mostly fog early in the day) prevented the kind of low-level flying required for CAS. Second, the planners of the operation made the strategic decision to focus bombing further inland behind the beaches. There were several different reasons for this. In Gallipolli, the invasion of Sicily and Anzio the initial landings were unopposed. It was only later that a counter-assault was made to push the invaders off the beaches. The other reason was German trench warfare doctrine in WWI, which the Allies assumed the Germans to still be using. This doctrine called for a weak front line consisting of machine gunners to slow down the initial assault and spotters to call down artillery fire, with strong secondary and tertiary lines to break the assault. Thus, the Allied assumption was that the beaches would be easy to take, and that it was further inland where problems would arise (problems did show up there, but that's a different story). I would dispute the ineffectiveness of the naval support. Several bunkers both on the beaches and inland were destroyed by 16-inch shells from the five battleships present, and counter-battery fire greatly helped the landing parties. In addition, the HMS Ramillies was instrumental in suppressing the German tank forces, which were supposed to form the spearhead for the counter-assault.

The effectiveness of naval gunfire against dug-in troops wasn't as great as some might think it is.

My source for this is James Hornfischer's The Fleet at Flood Tide He discusses the effectiveness of bombardment by battleships and cruisers during several landings in the Pacific. Hurling even really big shells in the rough direction of a dug-in target often didn't work that well. If a warship could see a target directly or if there was a forward observer adjusting shellfire onto a target then it was a different story, but it wasn't possible to just blast away at a beach and expect to kill everyone there.