Were the Yamatos simply prestige projects, or could they have deterred opponents?
Short answerThey could have become major deterrents if Japan had advertised them early, because their size and armament might have prompted allied caution and an arms race.
NotesThe class could look like an expensive prestige project, but a public launch and demonstrative commissioning might have made it a powerful deterrent. An advertised 18-inch-gun threat could unsettle American politicians while much of the forward fleet relied on 14-inch or 16-inch guns. Britain and the United States might respond with a new battleship race, perhaps completing Lion-class ships alongside Vanguard. Germany, Italy, and the Soviet Union would also have to react to the disclosure. Because Japan was regarded as secretive, admitting to such powerful ships could make foreign governments wonder what remained hidden. The effect would be political and psychological as well as tactical, and it remains a counterfactual possibility rather than a certain outcome.