The US Navy risked its battleships and carriers because they were confident they could be replaced, via production and switching ships from the Atlantic to the Pacific. The German navy, in both wars, tended not to because they knew they couldn't replace them. The Bismarck was the exception that proved the rule. The Japanese did not really risk their best battleships until things were pretty desperate.

The Bismarck and the Yamato in particular come to mind.

If you are looking for a WWII battleship that was too expensive to risk the Tirpitz is probably the best example. I think they let it out once.

Tirpitz did get used a few times, but it was mostly useful as a way to tie up a big chunk of the Royal Navy. Eventually, Tirpitz was sunk by aircraft.

The US's four Iowa-class battleships were quite useful, mostly for shore bombardment. They required a huge crew, 2,700 for WWII, Korea), and, after some modernization, 1,800 in the 1980s and 1990s. It's the crew size that led to their retirement. Each turret needed 90-110 people.

There was naval interest in building some "bombardment ships" intended for shore bombardment of countries that didn't have a significant capability for shooting back. But that went nowhere, since most of the US's enemies in recent decades have been too far inland.

The battleships proved incredibly vulnerable to aircraft. The Bismarck was disabled by a biplane, of all things.

The Tirpitz and also the major portion of the Italian fleet were able to exert disproportionate influence so long as they remained a potential threat.

https://en.wikipedia.org/wiki/Fleet_in_being#World_War_II

The Bismarck was sunk moving to its theater of operations. The Germans were very much planning to use it as a commerce raider, and it would have been a big problem for the allies in that role.

The Japanese government was afraid to send the Yamato into battle, but that had nothing to do with money (after all, its sister ship was deployed at the 2nd battle of Leyte Gulf). The problem was they'd used it as a centerpiece in their war propaganda, and they thought losing it would be a PR disaster that outweighed any possible utility in battle.

A few airplanes sunk the Yamato. It would have been far more effective if the Japanese had sunk (!) that money into better aircraft and better pilot training.

They had great pilots and great aircraft at the start of the war, but by the time Yamato was sunk it was all gone. They didn't even have enough fuel for a round trip - they were going to ground her and use her as a fixed gun emplacement.

> They had great pilots and great aircraft at the start of the war

A handful. Nowhere near enough. The Battle of Midway wiped out the bulk of them. The Zero rapidly became obsolete, too.