As I've posted before, I don't think the battleship (or the gun cruiser, for that matter) became obsolescent as a surface action asset until the 1950s. Until aircraft technology advanced sufficiently to permit night/all-weather strikes, the carrier remained a daylight-only asset and could be threatened by surface ships if operating without proper escort. Although, limited night/poor weather capability existed prior to the mid-1950s, it had not reached a level that would permit a naval battle to be fought under these conditions. It is an oft-repeated contention that the battleship was obsolete at the start of the war, or after 07 Dec 41, or even, as is sometimes seen in print, after Mitchell's testing in the early '20s, but examination of the technical capabilities of the equipment tends to point to a different conclusion. If the aircraft had achieved complete superiority, why were there so many major surface actions--including the various battles around Guadalcanal, in the Atlantic, in the Aleutians, at Leyte Gulf, etc.? Air power was notably absent during the engagement at Surigao Strait, just as it had proven relatively ineffective in stopping the night attacks of the Tokyo Express in the Slot.* The sensors & targeting equipment just wasn't ready to take on the difficulties of night attacks until much later.
The real reason why it is so easy to proclaim the battleship as obsolete before the mid 1950s is the annihilation of the Axis navies as a threat. The Soviet Union did not have a large conventional navy to oppose NATO surface warfare units until after the aircraft was ready to take on the night/all-weather strike duties. And there was the little doodad called the Atom Bomb that diverted development attention away from conventional strike warfare... The other factor is that social-political factors also shifted strategy away from the battleship as a distinct surface warfare combatant. The naval treaties so hamstrung design and build that cruisers ended up filling in for battleships and destroyers for cruisers. When the restrictions finally came off, we ended up with ships like the Iowas, Montanas, Des Moines, Alaskas, and Worcester--with all except the last weighing in heavier than HMS Dreadnought or any modern cruiser.
*Mentioning Leyte Gulf, TF34 was nearing engagement range of Ozawa's forces when it was turned back--too late--to intercept Kurita's Center Force. This would have been a daylight engagement, which would have been interesting. Perhaps another what-if thread that might prove interesting would be to discuss various surface actions and discuss the outcome if we replaced the heavy units on one side or another with equivalent carriers (say, substitute Independence class CVEs for Callahan's cruisers at Guadalcanal)?
Not that any of this has much to do with the original topic post...

Douglas