1. Again, the question is the great disparity of the Strategic value of each target. The Marianas were the key linchpin of Japanese inner empire, well within B-29 bombing range of the home islands, with all that entailed. Whereas Biak itself was valuable merely as a defense of the southern Philippines.
2. The Marianas also had great political value, as Saipan and Tinian were considered integral parts of the Japanese homeland, with Japanese civilians living there. The fall of Saipan brought down Tojo's government for this reason, in no small part.
3. The real problem, as you say, is that it makes little difference either way: if the U.S. now has fast carrier force that the IJN simply cannot defeat, it will roam at will through the Japanese empire, bringing along Turner's amphibious forces to pick off one possession after another - and Japan is doomed. But the IJN (and for that matter, the USN) did not realize just how great the disparity of power was between Mitcher's fast carrier forces and its own Combined Fleet. If they had, well... But they though that they really had a shot to damage it badly enough to force its withdrawal, which would leave the U.S. forces fighting on Saipan in a terrible situation.
The Japanese just had no good options at this point. But the longer they held off taking on Mitscher's fast carrier forces, the worse the encounter would end up being, given how rapidly it was being augmented with more ships, planes, personnel, and experience.