It's to create a standardized notation that works for theory. Another way to look at is why does b come after a in English alphabet? There's no need for the alphabet to be alphabetized but here we are.
Why white on right when setting up the chessboard

To prevent confusion.
Good luck with THAT.
Actually, if you turn the board 90 degrees and basically run the a-h files backwards, the game is totally offputting and disorienting.

Did anyone actually play a game with the white square on the left?
If you will, you would notice how the white king's side is completely destroyed if one follows a few 'by the book' rules.
No further comments your honours.
Interesting thread, by the time I got to the end I was thinking of the Star Trek episode 'Mirror Mirror'...

The main reason for always putting the white square in the lower right, is so that hundreds of years of analysis and chess literature, that make frequent references to the "light squared bishop" and the "dark squared bishop", and other references to light and dark squares, will be readable.
Actually, no.
Even into my early adulthood, most chess literature still used the terms king’s bishop and queen’s bishop. My medicare benefits just started, so I’m still young.
The rule of light on right is older than the practice of describing the bishops as light- or dark-squared.

Convention.
Why do runners circle around the baseball diamond counter-clockwise (so that First Base is on the right) instead of clockwise (with First Base on the left)?
Convention. We had to pick one. We picked one.

Convention.
Why do runners circle around the baseball diamond counter-clockwise (so that First Base is on the right) instead of clockwise (with First Base on the left)?
Convention. We had to pick one. We picked one.
I think most batters, like most people, are right-handed. And right handed people stand on the left side of the plate. If they started running forward, they'd naturally run to where first base now is, instead of making that kind of awkward quarter turn to head to third.
The main reason for always putting the white square in the lower right, is so that hundreds of years of analysis and chess literature, that make frequent references to the "light squared bishop" and the "dark squared bishop", and other references to light and dark squares, will be readable.
I also think that without that standardization, some players will visually/aesthetically grow to like one or the other orientation better. Then there would need to be rules regarding which player gets to choose.