Radar directed AA guns were totally a thing in the 1940s. The US developed the Mk37 director (using the Mk4 radar), and had it in service before Pearl Harbor.

Radar directed AA guns were totally a thing in the 1940s. The US developed the Mk37 director (using the Mk4 radar), and had it in service before Pearl Harbor. Carriers were invented well before this. And would have been invented regardless, as they were useful for more than just sinking battleships. The fact that they could sink battleships resulted in them becoming the preeminent surface combatant. But carriers were useful for scouting, for land attack, for defense against enemy aircraft, for anti-submarine warfare, for killing smaller surface combatants (like destroyers).