I agree that it would make more sense Go has a more mundane origin, have some roots related to simple commoner’s games. I looked up a lot of ancient sources and have some theorized evolving path for Go discussed here
Although I don’t feel it is the “difficulty” or aesthetic reasons of drawing squares prompt placing stones on intersections. Ancient unearthed Go boards are huge compared to modern boards. They can be up to nearly 70 cm on each side, and at least around 60cm with 17x17 or fewer “roads”. This matches ancient sources refering Go as 三尺之局 - a game of 3 ancient Chinese feet. However, the stones unearthed are about the same size as modern ones. To me, it is pretty obvious ancient players don’t view “inside the grid” as the place of contention, but the lines and intersections are.
Also, in my hypothesis, the precursor of Go, might not be a game played on a grid-like pattern board. But like Merels game where they are about the movement and blocking/capturing of stones. Where the lines indicate where the legal movement directions can be. This is also very telling if you saw a Chinese Chess board, also played on the intersections. With a weird “center of base”, I feel they are also a clue as to relics for earlier existing games why pieces are treated like markers, and moving on roads instead of occupying territory.
