I don’t think that handedness plays a huge role. I simply that in some cases it’s simply random, and in other cases it’s “I’m writing in this direction because that’s how I learned it”.

Inkwriting exists since at least the 2500 BCE, it was already used with hieroglyphs, and yet you see those being written left to right, right to left, boustrophedon, it’s a mess. Even with the Greek alphabet, people only stopped using boustrophedon so much around 300 BCE or so.

Plus if it played a role we’d see the opposite of what we see today - since the Arabic abjad clearly evolved among people who wrote with ink, that’s why it’s so cursive. In the meantime the favourite customary writing medium for Latin was wax tablets, where smudging ink is no issue:

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