During the 2 WW, the Navies of the world realised the importance of Carrier Warfare and Air Support for Sea Battles. But why did the advance of Carrier Doctrine go hand in hand with the disbanding of most big battleships? Barring a few exceptions like the USS Missouri, which was used as a floating artillery battery during the Gulf Wars, most modern navies seem to be comprised only of carriers, rocket cruisers, destroyers, submarines and small support vessels, while big battleships/-cruisers were either scrapped, mothballed or turned into museum pieces. What exactly made such big ships with awesome firepower unappealing to modern navies? Was there ever an effort to construct a nuclear powered battleship, like the US did with carriers like the USS Ronald Reagan? If not, why? Wouldn't modern technology like advanced fire controll, nuclear energy, new buildingmaterials etc. lend themselves to battleship construction, while making supplying these big ships easier than ever?
This question is not entirly of historic nature, but I think this is the most appropriate sub where I am most likely to recieve a serious and informed answer, not guesswork. I thank you all very much in advance, I appreciate the serious historic attitude of this subreddit above all else.
The problem with battleships, for the most part, is that they are much less able to deliver their firepower than carriers are. Some hard numbers are useful here. The longest-ranged hit scored by a British battleship came during the Battle of Calabria, when Warspite scored a hit on Giulio Cesare at a range of ~26,000 yards. The longest-ranged engagement by a British warship came in 1918, when the monitor General Wolfe shelled a railway bridge near Ostend at a range of 36,000 yards. The longest range obtained with a British naval gun was 51,000 yards, using a 14in gun in a high angle coastal mount and super-charges that never saw sea service. The first British carrier torpedo bomber, the 1917 Sopwith Cuckoo, had a range of ~160 nautical miles, or ~325,000 yards. In other words, the earliest aircraft carrier could deliver firepower to about six times the range as the best possible battleship. With improved aircraft designs, this ratio only goes up - and those aircraft can carry much more firepower too. An aircraft carrier is much more effective at fighting as a result; it can engage targets in a much greater radius and, as a result, damage or sink a battleship before it can get into rage to do the same to the carrier.
Equally, as technology advanced, the defensive advantages of the battleship went away. Armour-piercing bombs improved rapidly over the course of the war, obsoleting battleship armour. Guided weapons like Fritz X and HS293, as well as rocket-propelled weapons in development like the Uncle Tom rocket, allowed aircraft to score hits from outside the range of a battleship's own AA armament. The ranges of torpedoes, similarly, began to exceed the range of the light AA weapons fitted to battleships, and their warheads began to be able to overwhelm the torpedo protection systems. The introduction of the nuclear bomb completely negated any passive protection; no battleship could survive a nuclear explosion from short range. With these developments, battleships became as vulnerable as carriers were.
Given that battleships were as vulnerable as carriers were, and worse than carriers at doing damage, there was little reason to use them. They had large crew requirements, making them expensive to run day-to-day. They were very complex to build; the turrets in particular were some of the most complex pieces of machinery ever to go to sea. This made them expensive to build too. Carriers are much simpler to build, and while they do still have large crew requirements, carriers are more capable and flexible than battleships. A battleship is only really useful for shooting big guns at things nearby; carriers can strike targets ashore and at sea, provide fleet air defence, provide radar and ECM support and carry out anti-submarine warfare.