Ya, you have to wonder what the theory was behind building them. Japan focused a lot on their carrier/naval aviation. Obviously, the were the first ones to really use it to great affect, and if they had caught the US carriers in Pearl, the war would have taken another year two, heck, the Japanese could have invaded Pearl possibly, who knows.
My point is, how could they not realize that spending so much on 2 huge battleships was a little futile when they themselves were architects of naval air power at the start, surely they should have known that a single CV of their own would massively over match their own super capitol battleships so long as they didn't get within gun range, some 30 odd miles or whatever. Odd. Perhaps they were just in love with surface gun wagons, they did well enough with their cruisers, had some pretty successful gun battles with US ships especially at night, but that was years after they laid down the hulls for the 2 super ships. I would say that they started building them before anyone had seen what naval air power was truly capable of, that's part of it IMO.
However the comments about AA are true enough, the US learned its lessons and if you look at AA armament on ships in 41 and compare them to 45, there is a massive difference, the USN even purposely built large ships that were dedicated AA platforms.
I'll bet when the Japanese used planes vs Prince of Wales and company, they saw the writing on the wall for their own large warships, so far as using them in an offensive role without air superiority.
Funny how history repeated itself later, in some ways. The USSR built some large battlecruisers but never had any CV capable of launching more than crappy vstolv aircraft until late in the game, and then they only had...few, and they in turn had few aircraft that had crappy range. At least a war didn't happen to reprove the issue then.
