|"Your conclusions were all wrong, Ryan. Halsey acted stupidly."-Hunt for Red October
Well Ramius was not quite correct. Halsey was quite adept at the sort of "naval blitzkriegs" that marked the last stage of the Pacific War.
But on the most famous occasion he did act stupidly. At Leyte Gulf.
This is not just 20/20 hindsight. Arleigh Burke guessed at the time that Ozawa was bait.
However Halsey's mistake was not in attacking Ozawa. Even knowing that Ozawa was bait he should have done so. However the battleships should have been left behind to cover the invasion force. Halsey had more then enough to handle both goals but failed to practice proper economy of force.
The reason Halsey was right to attack Ozawa was that even if the Japanese succeeded, if the carriers were gone they had only gained a respite. But if the carriers remained the Japanese might have time to recover their air power enough to hold their own. If the Philipines fell to the Americans then the IJN effectively did not exist. Therefore it was at least equally important to guard the invasion force.
Something like this:
If invasion checked but carriers gone, Japan obtains useless lull
If carriers available but invasion successful IJN is finished. A navy is just as dead from lack of fuel and with more loss of face.
If carriers survive and invasion checked then comes lull, with small possibility of Japan temporarily regaining initiative.
And if carriers destroyed and invasion successful, then the rest of the war is large-scale "mopping up"(an odd phrase for Okinawa but in the staffie sense it is pretty much true-albeit it is one big "mop-up". This is indeed pretty close to what happend. But the frightful "near-run thing" could have been made assured with proper force budgeting.
And finally when the infamous, "the world wonders" message arrived Halsey turned back, out of pique apparently. It was to late to effect the battle. So he would be better off getting a good pursuit in. And indeed if he had, history might have been less resentful.