Perhaps we should ask ourselves also why the number "70" keeps cropping up in these traditions. It was the number of elders who accompanied Moses and Aaron to see the Lord (Exodus ch24 v9), the number of years of waiting time for the fall of Babylon (Jeremiah ch29 v10), the number of weeks in Daniel ch9, and also, of course, the number of disciples sent out in Luke ch10 v1.
My theory of the Biblical symbolism of numbers is that "7" is the number associated with God, and "10" the number associated with "completeness" or "the whole world". So that "70", as the multiplication of 7 and 10, would carry the significance of "the completeness of what God intends" or "God's work for his whole people" or "God's work for the whole world".
One or other of those suggested meanings of "70" would cover the examples I've quoted and also the Septuagint number; that could explain why tradition consciously or unconsciously drifted towards "70" as the "official" number of translators.