I have my own wacky theory why some scripts go from left to write, and it has nothing to do with reading, but with writing.
If you develop your writing system with pen, ink, and paper, and you write with your right hand, you’ll smudge the ink if you write from right to left since your hand will go over the freshly written letters. Thus, if you start your writing system at a time when you’d mainly be using pen, ink, and paper, you’d want to develop a left to right writing system.
Interestingly, the ancient Greeks started off with the Phoenician alphabet and probably the Phoenician writing of right-to-left, then later developed a Boustrophedon right-to-left-to-right system, and finally by the peek of Hellenistic civilization, adopted the left-to-right system which the Romans picked up.
Expanding on this crazy theory, if your writing system doesn’t involve pen, ink and paper, but painting on walls, using a stylus to make impressions in a tablet, or carving letters in stone, you might find it easier to write from right to left because you can start off with your right hand. Thus, the oldest Western writing systems were right-to-left.
The ancient Chinese also used pen, ink, and paper, but solved the smudge problem by writing from top to bottom. By the time you got back to the top of the paper, the letters would have been dried, and you could write from right-to-left. Other cultures who adopted the Chinese way of writing also adopted a similar method. Now, most Oriental languages now use a left-to-right, top-to-bottom direction.
Then again, this could all be due to random quantum fluctuations. The invention of writing is a rare event, and maybe when someone invented writing, they simply chose a random writing direction. Other cultures around that didn’t have a writing system simply borrowed what someone else invented. Thus, we have three random ways of writing which could easily stem from three random events, and what we see are other cultures around adopting whatever happened to be around.
I had a friend from Japan who told me that before WWII, all the street signs in Japan were written right-to-left because the Japanese wrote from top-to-bottom, right-to-left. Street signs were written the same way, but since were only one letter deep, each column only had a single letter.
After WWII, the Japanese adopted the Western left-to-right, top-to-bottom directionality. Thus, street signs were now written left to right.
In China, they mainly write left to right, but cars, buses, and plane are usually written from the front of the vehicle to the back. Thus, on the left side of a vehicle, the wording goes from left to right, but on the right side, it goes right to left. Sometimes, they do the same thing for the English, and you’ll see the English written backwards on the right side of a bus or truck.