It makes more sense that the sons of God, here, were the priests of the people of God.
Notice they were present at Sinai before the Law made the Levites priests:
Exodus 19 "Also let the priests who come near the LORD consecrate themselves, lest the LORD break out against them.”
Before this, there is no written provision for how priests were chosen.
We do see, in Genesis, certain names of children mentioned in the lineages and then "..other sons and daughters". These children whose names are mentioned: Seth, Enosh, Cainan, Mahalalel, Jared, etc., are literally "men of renown". They are named.
When we consider these two issues together we can see how certain people in their family, typically the oldest male, would become the priest of the family. They were the ones with the most experience about following God and living within His economy. This axiom is preserved in the reverence for elders even today.
So, if the "sons of God", people who preserve the ways of the Lord God in all things, chose to marry whatever woman they wanted, even those outside their own people, that would have disrupted the culture built by God's people. God would not have been pleased.