Respectfully, I'd disagree on that specification. The peculiar role of the aircraft carrier as a substitute for land based airpower was a phenomenon confined to the Pacific War. Elsewhere, there was less need for single engined attack planes when 2-4 engined heavier ones operating from land bases could do the job. As Astrodragon suggests, the advent of the guided bomb and heavy bomb in late 1943 puts the armour requirement for a battleship into the astronomical territory - the 96,000t Lion designs and the 106,500t Montanas. Prior to that, we saw Force Z attacked and sunk by 85 land based bombers, but it took until Musashi in October 1944 before carrier aircraft sunk a battleship at sea; the AA armament and ammunition situation for POW and Repulse in the SCS was suboptimal.
By the end of 1944, I would argue that not only the Pacific War was as good as won, but also the war at sea and the entire Second World War was as good as won. This wasn't the moment that killed off the battleship, which was already on life support. I would argue that the figurative 'Colonel Mustard in the library with the candlestick' was not October 1944, nor December 1941, although the latter would be set up as the seeming culprit in any good episode of Father Brown or Miss Marple and delivered a gut punch that sent Brother Battleship staggering about the place. Rather, the real death blow came with the guided bomb of mid 1943, which obviated the role of heavy armour before the atom bomb jumped up and down on its still warm corpse like a cheerfully homicidal 8 year old boy on an anthill. Aircraft killed off the role of the big gun as a means of offence, terminally dooming the 'all big gun battleship' epoch, but removing its defensive role as well did for it well and truly. Carriers don't enter into it.
The carrier based argument seems, in one respect, to be very much a Pacific War-centric/American-centric argument and interpretation of the broader Second World War, albeit an eminently understandable one and the same conclusion that others reach, if but by a more winding and scenic road.