I addressed this question several years ago in this discussion: Tafl game Alea Evangelii hints at 11th century go influence in Europe? - #4 by Conrad_Melville
Specifically: “I have been unable to find any theory about the origin of intersections versus squares in games, but I offer my own speculation, which I think is plausible and even fairly obvious. I suggest that badly drawn lines are less disturbing aesthetically than badly drawn squares, and therefore are easier to make and preferable to use for the common people in ancient times. Aristocrats, on the other hand, could afford to have craftsmen make boards with neat squares. The antiquity of Go is consistent with this, and I suspect that it originated among the common people (contrary to legend).”
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