But they didn't drive Essex class carriers close in shore, nor did they bring in the fast Battleships to bombard the shore. And shore bombardment was prior to an intended amphibious landing, not an attack on an airfield.
Carriers, you're right, the rest, not necessarily. The Japanese used Kongo-class fast battleships to bombard Guadalcanal with the express purpose of shutting down Henderson Field. They did stay well offshore, 10 miles or more.
Anyway, the real problem isn't bombardment, it's the use of CV ack to suppress a field. I agree with Waystin2 and the others who've said the solution is just to make the CV group stay further out and adjust LVT spawn range as necessary.
It might be fun to have bombardment groups with just cruisers and CVs. I think battleships are a bit out of the scope of the game, although they could be fun if properly implemented. What I'd like to see much more would be destroyers that could break off from the task group and make torpedo attacks. THAT would rock.
Smokescreens would be cool too.
As for the ship gun sighting and aiming systems, the RL ones were actually
more capable. The biggest lack in the AH system is not having rangefinders or fire control computers (although our sights do contain a limited computer function in sea mode, it's not as capable as the RL ones). The thing that makes ship gunnery easier in AH is the lack of weather or any other obscurement of the target (like the above mentioned smoke) - that, and we bring task groups much closer to each other and their targets than was generally the case for battleships, cruisers, or (rarely) carriers in daylight surface battles. Our "optics" are a little better, but the naval gunnery optics of all the major navies were of extremely high quality.
They generally didn't ever bring warships to a complete stop during combat, but for gunfire support they did slow way below the flank speed our TGs always move at.
I'm not aware of any battleships that were driven off by shore-based batteries, but I'm also not aware of any battleships that got within range of functioning shore-based batteries of battleship caliber. And of course our ships aren't battleships. There were a number of instances of cruisers and destroyers being sunk, mauled, and/or sent packing by shore defenses, including the German naval assault on Oslo (although it was captured shortly afterward by troops who were airlifted in) the first Japanese attempt to take Wake Island. Shore batteries worked, that's why they invested so much in them. Where they didn't work it was usually where the attackers, particularly the Allies in the late war, brought in hundreds of ships and simply overwhelmed the defenses by sheer weight of numbers. Maybe if we beefed up AH shore defenses we'd get to see multiple TGs coordinating to take a target more often.
(As I side note on the effectiveness of shore-based batteries, and because I love any excuse for talking about my ancestors, the only reason Richmond remained Confederate in 1862 was because the heavy naval shore batteries just down the river at Fort Darling on Drewry's Bluff, with support by field artillery and the infantry of my great-great-grandfather's regiment (the 26th Virginia), managed to drive off a Union attempt to force the river defenses, including the ironclads Monitor, Galena, and Naugatuck and a couple of wooden ships. Galena was just about pounded to scrap metal by the fort's 8" and 10" Columbiads, the federal ships were forced to withdraw, and Union Gen. MacClellan took an eastern land route toward Richmond and what would become Lee's first great victory, the Seven Days Battles.)