Strategic is a good word as it brings up an important comparison with nuclear weapons in the 20th century. There was only one conflict in the 20th century where nuclear weapons were used on the battlefield, does that mean they were useless? Hardly, nuclear weapons are obviously devastatingly powerful, but for that precise reason there is a reticence to use them directly. Instead of shaping the evolution of events directly through their use nuclear weapons shape the evolution of events and battlefields through their existence. The same was largely true for battleships as well for a good chunk of the 20th century.

Dreadnoughts and later battleships were such overwhelming weapons for a period of time that they shaped geopolitics, naval policy, and naval tactics just due to their existence and presence more than their direct use. Both geopolitics and war tend to have aspects of a complex game like chess where it's important to make moves which are designed to forestall or effect certain specific future moves. If you, as the Allies in WWII, are certain that the consequences of, for example, the German Battleship Bismarck breaking out into the North Atlantic are expected to be disastrous then you put forward great effort to sink the Bismarck before that can happen.

The key advantages of the all big gun battleship design go beyond merely the increased firepower and penetration capabilities of bigger guns. Perhaps the most significant advantages are more accurate fire and longer engagement ranges. Distance has always been the best defense on the battlefield throughout history, and being able to engage an enemy at a distance where they cannot engage you, or even just having significantly improved effectiveness at a given range is a huge advantage on the battlefield, equivalent to tonnes and tonnes of armor. That's particularly why battleships were such fearsome weapons, because of the potential for them to engage with vessels that could not even engage in return and would be like so many lambs to the slaughter if they did so.

For a time battleships were predominant strategic naval weapons, because of the potential for a state of the art battleship to be nearly unstoppable against lighter armed opponent ships. For that reason much of the naval world revolved around them (including the first strategic arms limitation talks in the form of the Washington Naval Treaty), even though actual head to head engagements involving battleships were extraordinarily rare.

That said, by the time of WWII the battleship was essentially entirely obsoleted by air power. Moreover, there's a case to be made that the presumed dominance of the battleship in naval affairs during the early 20th century was a bit overblown. For example, British battleships were so poorly (dare I say incompetently?) run that they were enormously vulnerable to being hit, so much so as to nullify much of the supposed protection of being heavily armored. That said, they were still very imposing weapons during the roughly four decades where they were dominant. Had they been used to their full extent in warfare at any given time the naval battlefield would have been significantly shaped around them, the actions they took and the reactions to their presence.

Having a threatening battleship meant locking up a significant amount of resources of the enemy. For example, the U.K. had to put a relatively considerable % of its Royal Navy and some of its R.A.F. basically on hold, in case either the Tirpitz or the Bismarck got too close to British shores. Although those two ships never actually had any relative amount of real engagements with British ships, their presence alone, and thus the possible threat of them meant the British had to hold back some of its force (which of course would have been more useful elsewhere) in case the German battleships actually decided to strike.