How ancient players view and record a game
The stones on top don’t matter, they are just markers. The locations, the intersections, are the concept behind, not to “occupy a square”, but to control intersections of roads. What matters isn’t the area encircled, but how well establish these connections are. How to better visualize the area wasn’t the top priority in our ancestors’ minds. And from my digging and hypothesis, I don’t think the original goal of the precursor games that evolved to Go is about encirclement at all, There are solid evidence and traditions to know that before the time Go was spread to Japan, the goal was about how many stones to “live” on the board. The bigger encircled area is just convenient for not having to play until the board is filled.