Why smaller fast battleships do not solve Japan's problem

Could Japan have built several smaller, very fast 410 mm battleships from 1931 instead of the Yamato class?

It was technically possible, but industrial displacement, treaty reactions, and Japan's need for heavy fighting power make the proposed small fast ships a poor simple substitute.

Building smaller Scharnhorst-sized ships more quickly would still consume Japanese machinery and yard capacity that could otherwise produce carriers and other warships. Starting in 1931 also means abandoning the London Naval Treaty early and provoking British and American construction. A faster conventional nine-gun design could be more useful than Yamato's extreme scale. A six-gun battlecruiser, however, does not fit Japan's expectation that its line must eventually fight a superior enemy fleet.