The Menuki was ALWAYS on the palm side, relative to the dominant hand of the swordsman. From Heian until Edo. In Edo it changed. The obvious reason (and it took me a few hours to visualize), is combat grip. Koto gloves. Snow Rain Ice Mud Muck and Blood, all things encountered on modern battlefields, from antiquity until today. Same consideration. It is not just hockey players that modify their stick for grip, baseball players, but many others that depend on grip. Tennis players. Be it they play in ideal conditions.
Even in cycling, below 10C, with speed, sensation is lost fast. The gloves and handlebars require a good feel as most motions are done without looking down.
In battle condition, with kotos, the hand is actually bigger and there is a significant decrease in grip. The Menuki, and its texture, helped with grip, as well, of course, to orient the blade, such as nightime. Am sure quite a few took a swing and the blade twisted. If it was night, it may not be easily obvious. With the Menuki on the palm side, this became an easy fix.
During Edo, Samurai became refined gentlemen and bureaucrats, and combat grip considerations subsided. Kotos became a thing of the past. Quite possibly, Japanese hands were too small for a tsuka with Menuki (again, a non-issue with Kotos), so it was moved to the finger side.
