The issue isn’t battleships vs aircraft carriers: the issue is control of the air.
Surface ships without air protection were vulnerable to air attack: the Japanese gave a very convincing demonstration of this early in the war, sinking two armored British warships (Repulse and Prince of Wales). And unlike Pearl Harbor, The British ships were at sea and underway, capable of maneuver and prepared for air defense. And yet they were sunk … quickly.
Carriers themselves were vulnerable to air attack – though they proved more durable than many expected. But they could also deliver offensive blows from hundreds of miles away, long before heavy ships had closed to within range of island objectives. So one of the primary tasks assigned to the fast carrier forces was the destruction and suppression of enemy air forces. The fast carriers would sweep in ahead of the landing and bombardment forces, seize control of the air, and maintain control of the air until local ground-based forces could take over. This kind of offensive strike was the best possible defense, both for the carriers and the heavy ships.
Carriers and battleships were fundamentally different weapons. A heavy ship could only throw its ordnance a few miles; a carrier could strike targets hundreds of miles away. A heavy ship had to stay in close proximity to its objective. A carrier 200 or 250 miles out had thousands of square miles of sea to disappear into, and would still be in striking range of its targets. The fleet carriers held the edge in terms of raw speed and maneuverability. And they were more difficult to put out of action than anticipated. A ship that’s hard to find, hard to hit, and capable of delivering heavy blows from hundreds of miles away is a formidable weapon.
The quick fix for these facts is the optiional rule “Air Supremacy”:
Air Supremacy
Fighters attack or defend in the opening fire step of combat if no enemy fighters are present or remain in combat.