If Herodotus said that Homer did not write any of the other Epic Cycle poems, would that not point to Homer’s authorship of the two attributed to him?
Why would Herodotus, or any other Greek of the fifth century, know anything for sure about Homer’s authorship of the Iliad and the Odyssey? Greeks of the classical period thought they knew many things about the Bronze Age which are now considered unproven legends. Thucydides thought he could use details in Homer as historical evidence.