In terms of the Runescape’s history, the Godswords were not created until the end of the Third Age. Since Nex and her armies were imprisoned early in the Third Age, it wouldn’t make sense for her to drop a Godsword.
Spoilers for those not aware of the lore:
Nex was initially imprisoned in the early Third Age, before the Godsword was made. However, as mentioned in the blog, she later briefly escaped her prison towards the end of the God Wars. This was right in the middle of the fight over the Godsword. When the four armies joined forces against her, Nex was very eager to turn their own weapon against them.