>>64441815
They did (see pic rel) however in addition to >>64442619 points, there was also the fact that Shinano sank circa 3 hours afterward and the fact that keeping the periscope up long enough would increase the risk of counter-detection from the escorts.
Per the wiki for Shinano, she had apparently already detected a radar sweep from Archerfish, but thought she was operating as part of a pack and acting as a decoy of sorts