Personally, I do NOT believe the successful sinkings/cripplings of battleships at sea in WW2 by aircraft say a lot. In almost every case, the ships were steaming alone or virtually alone without a large escort force and without effective air cover. Put 5-10 Iowas or Yamatos jammed packed with AA at the center of a defensive box surrounded by DD's and CL's, put a carrier or two in the mix to provide air cover and I would dare any WW2 air force armed with dumb bombs or crude radio controlled glide bombs to sink them. Heavy bombers with their Tallboys or Grandslams in particular woudn't stand a chance.
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Your post actually illustrates why the BB didn't survive as a major fleet unit. Even with 10 of the most powerful warships ever made (actually four more than the U.S. & Japan built together), surrounded by escorts, you still need to add a couple carriers to ensure survival. Why not just make it 12 carriers?
The real death knell for the battleship, as a primary weapon system, to a support system, wasn't at Pearl Harbor, or even off the coast of Malaya, in December 1941. The battleship lost her crown, once and for all, on October 24, 1944, when the USN aircraft sank
IJN Musashi, in open water northwest of Leyte, while in the company of 3 other battleships (including her sister the
Yamato) eight heavy cruisers, two light cruisers and thirteen destroyers. This is,
sans aircraft carriers, almost the exact Battle Group described above. Despite the large, well armed and very strong escort,
Musashi was blown out of the water by three deckloads of USN aircraft. While the strike wasn't as effective as it could have been, had say, 12 carriers, been available to mount the strike the largest warship in the world sank, despite the presence of 23 escorts and three other battleships.
Surface ships, without robust air cover, were meat for aircraft by 1942, by 1945 they were barely an irritation, as illustrated by the end of the
Yamato en route to Okinawa, where the commander of the American Task Force couldn't even
bother to detach a surface force to sink her.
This being said, there is still a number of roles for battleships, even today. These are not as the centerpiece for a navy, but as a role player of great importance as part of large navy (which these days means only the USN). These roles go from gunfire support (127mm guns for shore bombardment? Please), to cruise missile platforms to escorts that can keep up with a carrier regardless of weather.
You can create this in a single package, probably around 65,000 tons, nuclear powered, with one, perhaps two, turrets with 16"/406mm main battery, AGEIS or improved AGEIS sensors, towed array, VLS (6-8 61 cell launchers), hanger space for four helos/UAV, and modern armor. It would be expensive as hell, probably $3 billion a copy, but it would provide an exceptionally flexible, very rugged platform that would greatly enhance the defenses of a CBG, and would allow engagement, by the BB, out to 1,000 miles inland, and a strong ASW presence.
Will we ever build one? No. Partly because we'd need one per carrier (with a few extra) & at $3B each the Navy would never get Congress to bite.
Pity.