I still haven't heard of any weapon system, besides a hardened silo in Nebraska that can take the kind of punishment that a battleship can. And a hardened silo can't move! As for the 'claim' reference the Bismarck, did aircraft sink the ship? No, they did not, it was surface ships, including two battleships that sank the Bismarck. Yes, aircraft MIGHT have been used to do so, but in point of fact, they were not (nor is there any guarantee they would have been able to hit the ship anyways, given how much Bismarck was slewing around). As for 'the end was known by the end of WW1,' if that was the case, then why were SO many huge new battleships and battlecruisers planned and started? Only the treaties, pushed by the Brits, stopped the battleships. As for Mitchell getting his 'chance' to bomb the old German battleship, anchored, unmanned and unarmed, and never designed to deal with aircraft in any way, Mitchell had to fight to get that opportunity! And even though he DID eventually sink it, if battleships were therefore 'instantly obsolete,' then why did everyone continue to come up with new designs and new production? Why were the old battleships sunk at Pearl Harbor raised, modernized, and put back into service just as quickly as possible? Same for the Italian battleships at Taranto, for that matter.... Not the sort of treatment you would expect in wartime for a heavily damaged and 'obviously obsolete' weapon system!
Again, the reason there were no battleships built after WW2 was simply because no-one else besides the US could afford them, and the US had such a preponderance in everything, that there was no chance that any other nation could possibly 'catch up' to challenge the US in a naval arms race. As the US battleships very quickly HAD no equivalent opponents to deal with, there was not a lot of reason to either keep them in service, or create new ones, just keep the ones they had and periodically update them as needed. The industry to produce battleships and most particularly, battleship armor all disappeared, either victim of the massive destruction of the war years (Europe and Japan), or conversion after the war to other production (as was the case with the US). There is currently no foundry or steel rolling mill in the world that can produce large armor plates 12" or more in thickness (hasn't been for more than 40 years), and the cost of reproducing such an industry is so cost-prohibitive, that it is highly unlikely that anyone will ever build a battleship from scratch again. But again, that does not mean the battleship is, or was obsolete; it means it has been SO successful, that at least in the case of the US Navy, it has defeated ALL challengers, and can therefore retire gracefully, as no further challengers have arisen, or are likely to. Not torpedoes, not kamikazis, not bombers, not missiles, not submarines, not carriers, and not nukes. Funny how often those old battleships keep coming out of mothballs periodically for new duty; I don't recall any old submarines, or old carriers, or old cruisers, or old anything else coming back into service after decades, can you?