Heh...... The battleship was made obsolescent by the AIRCRAFT CARRIER. Not WWII battleship was ever even HIT by guided missile fire, because guided missiles DIDN'T EVEN FLIPPING EXIST. Not until '44. maybe even '45, when the Germans deployed a radio-guided flying bomb. And even that wasn't a missile, it didn't have a rocket engine. It was a primitive JDAM, basically.
The battleship: Pinnacle of the gunships, capable of killing its foes almost as soon as it can see them. Capable of smashing through hulls, destroying machinery, obliterating shore positions from twenty miles out to sea.
The aircraft carrier: The last capital warship. Capable of finding, tracking, and killing its targets without even getting into radar range. Capable of deploying torpedoes, bombs, and gunfire from almost two HUNDRED miles from its targets. Capable of utilizing every ship-killing method a battleship's entire fleet can use (The Japanese used 16-in armor-piercing shells with fins for Pearl Harbor), and then some, all without the captain ever seeing the enemy.
The battleship was doomed. It couldn't match the range or the sheer killing power of a carrier's squadrons. Battleships sank, one by one, due to air power. There were a few remaining gun duels. A few ships sunk by battleships. A few battleships sunk by other battleships, or by battleships and escorts, as was the Bismarck, but no battleship fleets would ever again meet in a grand, Jutland-esque duel on the high seas. The carriers could kill them first. And kill them they did.
The mightiest battleships ever put to sea: The Yamato and Musashi: Sunk by carrier-borne aircraft. They took bomb after bomb, torpedo after torpedo, but they finally sank. Because they couldn't shoot the ships responsible for the attack.
If you think that guided missiles were a factor in WWII, or the death of the battleship, you are mistaken. Battleships were too expensive, carriers could do what they could do with less risk, and more effect. Because a carrier can destroy a battleship, while bombing a shore installation, while covering its task force from hostile fighters, while hunting down the rest of its enemies....simultaneously. A battleship is only good for one thing: Doing battle. And when there is a ship that can do it all, better, and do more as well, there is no choice.
The battleship was doomed from the moment that the Japanese sailed for Pearl Harbor, damaging or destroying all the working battleships of the Pacific Fleet...forcing America to prove that the carrier had quite the future ahead of it. It forced new tactics on the ambushed navy, forced them to explore the true extent of what could be done with a carrier. And it was revealed that the carrier could do it all.
No new US aircraft carriers were built post-war because America was trying to reduce military expenditures and stuff, not get more of something they already had a HUGE lead in.
HUNDREDS of carriers (Including escort carriers) were built in WWII. HUNDREDS. Including over a dozen fleet carriers (The biggest size, until nuclear-powered supercarriers).