By the time the U.S. felt it was ready to go onto the offensive in the Central Pacific (late 1943, after the attritional battles in the Solomons had been won, and new carrier construction was reaching the fleet) Wake was no longer critical.
Tawawa provided a deeper incursion into the Japanese defensive perimeter, and provided the follow up assault against the Marshalls a better logistical support location. Once the Marshalls were taken/cut off, the strategic importance of Wake evaporated.
Wake was a strategic linchpin for the Japanese, not for the U.S. If the U.S. had been able to deny them Wake in the opening events of the war, it would have seriously undermined Japan's positions in both the Marshalls and Marianas. Once the U.S. took the Marshalls the Island became a backwater.