“They couldn’t get enough fuel to the front fast enough to get the Yamato to run on regular missions as well as the rest of the fleet.”
Not quite true...
The Japanese solved this problem for most of the war by stationing the battlewagons at Brunei, close to both the oil, and the refineries.
It was only after the fall of the Phillipines that this became untenable, and the surving big ships returned to Japan.
Also, Yamato was heavily damaged in 1943 by a torpedo hit that almost sunk it. It made her captain and crew aware of how important Damage Control was to modern fighting, and they trained heavily for it, one of the few IJN ships to take it seriously.
Except the Yamato was never at Brunei. It spent most of the war at Truk, about
Yamato’s officers and crew may have been aware of damage control issues and trained for it - but the problem is the vessel was not constructed with advanced damage control in mind. A hit that a South Dakota could take and keep fighting due to the damage control technology built into the ship would have (and eventually did) gut Yamato. Same reason why when our carriers took the same kinds of hits that sunk the major IJN carriers, they didn’t. For example, using your aviation fuel tanks as structural elements of the hull is generally a BAD idea, yet the Japanese did exactly that with their carriers.
A good example of just how important damage control was, look at USS Gambier Bay during the Battle off Samar. Yamato closed to point blank range and pounded the crap out of Gambier Bay, a tiny escort carrier. Despite relentless fire from Yamato and the rest of the IJN fleet, the carrier held together long enough for almost 800 of her compliment of 860 to get off - she stayed afloat for almost an hour after Yamato finally got her range, and 17 minutes after the abandon ship order was finally given. The reverse scenario, a Japanese carrier caught by a surface force, usually ended up being over very quickly with few survivors.
Er, Yamato spent the war more than 4100km/2100 miles away from Brunei. Fuel had to be tankered out to her, and by the time it got there, the local command had to decide whether they’d fuel Yamato or the rest of the fleet that was there.