The transition from the dominance of the battleship to that of the aircraft carrier is definitely far more complex than it's usually envisioned. Most pop-history tends to portray it as a clash between old "big-gun" Admirals stuck in the past, while ignoring the "obvious" genius of air power advocates. In many ways, when we consider naval aviation in the inter-war period, we look at it with the benefit of substantial hindsight, with the overwhelming dominance of air power in 1945 and beyond clear in our minds. Yet, when we consider the perspective of naval designers in the mid to late 1930s, what for them would be the future was highly uncertain.

Throughout much of the inter-war period (1920s and most of the 1930s), the airplane was far less capable a weapon system than it would be even a decade later. It is difficult to express just how quickly aircraft technology advanced in that period. While much is made of Billy Mitchell's of 1921 air strike demonstration on the German battleship Ostfriesland, it's important to remember that the attacks were against an immobile defenseless target. Moreover, carrier launched aircraft throughout this period were short ranged and capable of carrying a very limited payload (hence why many carriers built in the 1920s and 30s maintained heavy guns, as it seemed entirely possible carriers would be operating close enough to the enemy fleet that there would be a risk of them becoming engaged with enemy cruiser forces). It was only later, in the build up to the war itself that aircraft like the Japanese B5N, G4M, D3A and American SBD Dauntless that were capable of carrying a payload large enough to deliver serious damage to capital ships and with the range to strike from far enough away that the risk of a surface engagement was negligible. Part of this was also the development of the tactics of both dive bombing and torpedo bombing, but I won't get too much. The point is though that in a very short period of time, aircraft advanced from biplanes of questionable utility in a naval strike role to a far more powerful, but still untested tool.

That is not to say that naval aircraft didn't have a role in the eyes of naval officers around the world throughout the interwar period, but rather it was a question of how substantial a role they should play. For most navies, carrier aircraft were envisioned as strong supporting arms to the fleet, capable of both long range scouting operations as well as slowing down and damaging capital ships, but not necessarily of deciding battles themselves. Indeed, even when we look at the war record of the early parts of World War II, no battleship was sunk while at sea in combat operations until 1941, when the Japanese sank Prince of Wales and Repulse. Even this was via land based rather than by carrier aircraft. The British air attacks against Bismarck and Vittorio Veneto did not sink their targets, but rather damaged and slowed them down, forcing the latter to withdraw, and exposing the former to destruction by a surface force. Meanwhile, the attack on the Italian fleet at Taranto was similarly against moored, stationary targets, rather than a fleet at sea and ready for combat.

Suffice it to say, in the 1930s when both the Bismarck and Yamato were designed, it was hardly an obvious fact that carrier aircraft would rule the seas in the next decade. Battleships remains an entirely sensible investment. While the potential of the aircraft was clear, they were--nonetheless--a risky investment should they prove less capable than envisioned, and so navies around the world continued to build battleships as well. Thus, to answer your question in the short form: the idea that the Yamato and Bismarck class battleships were "obsolete from the day they were launched" is a bit of a vast oversimplification of history. While there is substantial criticism that can be laid in the actual engineering of both ships, the concepts behind battleship were not necessarily obsolete in the late 1930s and early 1940s. The obsolescence of the battleship in its entirety did not really come until--I would say--the post World War II environment, where the vastly increased range and payload capacity of carrier aircraft meant that the power of a battleships guns was effectively made irrelevant, and it was no longer worthwhile to build such ships, when carrier aircraft could do the same--if not more--but from even further away.