Why does adding "in reading order" reduce mental effort compared with the schoolbook method?

It minimises what you must hold in working memory — one running total instead of a column of digits plus pending carries.

Working memory is the bottleneck in head math. The right-to-left paper algorithm forces you to remember carry marks while you keep processing, and it produces the answer backwards. Left-to-right (and compensation) collapse the problem to a single evolving number that you refine from most-significant to least — so you can even start saying the answer before you've finished. Fewer items held = fewer chances to slip.