What are the benefits of a language being written to the right?

Neither is better or worse than the other, each works how it needs to for its language.

Japanese was written vertically, so characters are ordered from top to bottom while it is the lines which are separated from left to right. The slow leftward advancement allows a person writing on a scroll to write with their right hand while unrolling the scroll gradually with their left. In modern times you can write Japanese horizontally, but in that case you usually write from left to right. Characters written horizontally from right to left is only done in exceptional cases.

I don't know if there is an advantage or disadvantage. There are other writing directions as well. Like boustrophedon, which starts in one direction, and then when you get to the end of the line the next line goes the other direction. This sounds like a better way to write to me!

Egyptian hieroglyphs can be written either RTL or LTR, you tell because the animals and humans in the script face the beginning of the line.