The left to right writing thing is more to do with the introduction of pencils and pens. Japan had the same thing.
With a brush you can write top to bottom, right to left, because your hand doesn't rest on the page. With a pen, you are going to smudge what you just wrote. With a pencil, you will get the lead on your hands.
Interestingly one of the reasons why Japanese computers were often more powerful than Western ones was that they needed to have better graphics to show complex characters, and so the standard design was to have separate CPU and video memories. Western machines usually had a unified architecture where CPU and video shared a single bank of RAM, limiting the bandwidth available to both.