Back when I was in high school a friend told me that the ancient Greeks, at one point, had written both left to right AND right to left, alternately. You can see where this would be efficient for speed reading. Scholars call it "boustrophedon", which means "ox-turning", as when you plow a field with an ox, and you turn and go back the other way, still plowing.
The individual characters are mirrored, like Leonardo Da Vinci's famous "code". I actually taught myself to do this, also in high school. Maybe I had too much time on my hands in high school!
Recently I read that it was boustrophedon that accounts for the transition from Right-to-Left to Left-to-Right writing! The Semitic languages (such as Hebrew, Arabic, Phoenician) are all Right-to-Left. The Greeks took their alphabet from the Phoenicians.
'Greek was originally written predominantly from right to left, just like Phoenician, but scribes could freely alternate between directions. For a time, a writing style with alternating right-to-left and left-to-right lines (called boustrophedon, literally "ox-turning", after the manner of an ox ploughing a field) was common, until in the classical period the left-to-right writing direction became the norm.'
But... while that explains the ability to shift readily,
it doesn't explain why they chose Left-to-Right steadily.
it was commanded
because Left-to-Right is better when working with ink,
at least for the right-handed.