I think the decisive rolls that battleships of any kind played in WWII were few and far between. Tirpitz was best used as she was, a decoy/threat-in-being to tie up resources, effectively removing them from other areas. Bismarck was a colossal waste of material and manpower. The Japanese sorely needed to go back in time and make more carriers in place of the Yamatos. The Italian battleships achieved nothing. The French battleships achieved nothing. The British battleships achieved little in return for the manpower and resources they consumed. The far east fleet lasted 3 days. The Mediterranean fleet did a little better with Hood and Warspite achieving a little success against the surrendered French fleet and the Italians respectively.
I'm torn because I love battleships as 'things', but as weapons they were particularly useless in comparison to the wealth, material, and manpower they consumed. Just look at the material wasted by the Germans on the High Seas Fleet in the first world war, not to mention that the existence of that fleet at all was partially responsible for Britain feeling paranoid enough to join in the fight against them. I'd even suggest that without the High Seas Fleet, Britain would have not been eager at all to defend the continent. Much of the animosity between the two nations was built upon the potential threat to naval supremacy, when I feel that the Kaiser really just wanted toys like his cousin had. Seems the rulers of empires are not all that different from men and their big speakers. You need big ships or you're not manly rulers. Despite whether its the best tool for the job.
Hitler would have been better off building more submarines or investing in a more competent strategic bomber force. Or building more and better tanks than were being built at the time of the Bismarck and Tirpitz' construction. The greatest victory I can think of for US battleships was in the Philippine Sea when they put up a wall of 5" anti-aircraft shells with deadly effect, as much due to shell technology and centralized gunnery control and the VT fuze, as to what the guns were mounted on, to decimate the air wing of the Imperial Japanese Navy for the last time. But carriers played a bigger part in that battle, and what did the 16" guns do?
As bombardment machines, cheaper, slower, less manpower intensive ships could have gotten the job done. The large ships were steadier gun platforms but it still seems that however long the battleships spent shelling a place, that there was still stiff resistance when boots hit the shore. I think the presumed affect of shelling was overrated in almost every invasion. Iwo Jima was not a big island and they shelled the hell out of it, but the caves were so extensive that much of the defenses survived.