I have to read that only have read/watched snippets of this battle.I do remember reading US Naval forces didn't have an over all Admiral at this battle and evidently neither did the IJN.So the order of battle was really uncoordinated.Some of the forces were under Nimitz/Halsey and others still under MacArthur(mistake IMO) and efforts disjointed.Should have left Nimitz orchestrate as he got them that far.However Halsey did get suckered into some well planned ruse and the 7th fleet was having their own problems also.But then things weren't going so well either for the IJN.Big messy boat brawl really
The fundamental problem was that the Philippines was at the convergence of MacArthur's South-West Pacific Area command and Nimitz' Central Pacific Area command. Neither of them was put in overall command, so we did not have unity of command at the level where operations turns into strategy. Halsey's 3rd Fleet was under Nimitz' command, while Kinkaid's 7th Fleet was under MacArthur's command. This sounds funny, but it wasn't. MacArthur had been fighting in New Guinea and the Solomons, and 7th Fleet was the "navy" assigned to him. In the same way, while Nimitz' ground striking power was mostly Marines, there were also Army combat units assigned to his command, increasingly so as the war went on.
The problem at Leyte Gulf was that the two theater commands were just cooperating rather than working under the same commander.
So the "Taffy 3" fight off Samar was fought by elements of Kinkaid's (MacArthur's) 7th Fleet, as was the battleship fight at Surigao Straight, while the carrier battles (sub-battles of the overall battle) were under Halsey, who worked for Nimitz. And Halsey got a little froggy at the chance to destroy the Japanese' last carrier fleet and was decayed away from Leyte Gulf chasing empty carriers.
Back when the Army still emphasized "principles of war," one of the most important was Unity of Command. When you don't have it, there is a greater chance for things to go wrong once the enemy starts doing things not anticipated in the plan. One of the most glaring flaws exposed in the April 1980 "Desert One" attempt to rescue our hostage in Iran. There were USAF special ops C-130s, Army Delta Force and Rangers, Marines launching from Navy ships flying Navy helicopters, and nobody in overall charge who could talk to everybody else.
Same problems were exposed in the Grenada invasion, and we ended up having some of our troops in the 82nd Airborne Division killed by USAF A-7s strafing a brigade tactical operations center (TOC). They were using different maps with different sets of coordinates and were not talking to each other by radio.
Anyway, back to Leyte, that was the problem off Samar. The fleet carriers with the airpower to do something against Kurita's battleships were not talking to "Taffy 3" because their chains of command went back to Pearl Harbor and Australia, respectively.
Strategically, we could have bypassed the Philippines, but MacArthur had promised that he would return, and the Philippines were an American commonwealth, so national honor and good faith were involved.