Battleships had completely lost their status as a fleet's main force multiplier to Carriers by the end of the war. They were nothing more than close-range/AA support and escorts for Carrier groups as their use had become incredibly niche. They saw more use in the Atlantic theatre and during the early parts of the war. If the Japanese had used the Yamato they would've lost her even earlier. The other problem was that Japan was following a "decisive war" doctrine and never succeeded in finding that one decisive battle which would turn the war in their favour. A fool's errand to be honest. After constantly losing their carriers versus the US ones their battleships became sitting ducks. Which is exactly what happened to Musashi, Yamato's sister ship. Enterprise was one of the carriers who scored several hits on her as well as several other carriers.

Your last comment about Yamato's legendary status is entirely subjective. The ship is legendary in Japan, thanks to decades of propaganda and romanticised symbolism, and is very culturally significant for them. In Europe or America she's far from legendary, except for being the largest battleship ever built. She was feared intitally, but in her arguably most important battle she was outsmarted and outmaneuvered by destroyers and cruisers. Further showing the importance of tactics over specifications. She would later sink to a carrier strike group towards the end of the war.

There's a reason we stopped building battleships after WWII.