The real problem is that choosing to divide the galaxy into 4 quadrants is not just arbitrary, it's also silly in that it doesn't follow any "natural contours" of the Milky Way.
This critique only makes sense if the four-part division of the galaxy was the only way that territory was perceived by the UFP. Yet there are numerous territories that are referred to throughout the franchise: the Typhon Expanse, various empires, the Neutral Zone, various star systems, the Badlands, etc. Some of these are astronomical features, others are political. Some are defined by the great powers, others by the people who live in them. Obviously, the lines of longitude and latitude, to which the Greenwich line refers, would seem arbitrary if there weren't other territories that were under consideration, natural or political: continents, river systems, mountain ranges, nations, provinces/states, counties/departments, etc. Even though the lines of longitude and latitude create a global paradigm of spatial arrangement, I don't expect to turn on the news tonight to hear about what's going on at 36°13′N 37°10′E, but at Aleppo.