There is a difference between looking for to engage another task force in battle, and looking for a direct sea battle. The U.S. fleets were looking for the Japanese fleets in order to attack them with their aircraft. They were not looking for the Japanese fleets in order to engage them in a direct sea battle. The U.S. fleets lacked heavy battleships at the time, and would not have fared well at all in a gun duel. Later, when the new U.S. battleships had joined the fleet, and the resurrected ghosts of Pearl Harbor were there as well, Halsey, at least, was actively seeking a direct sea battle and a gun duel with the Japanese.