All quadrant boundries are arbritary anyway. Rather than split it in a grid like "+", they could have split it into grid like "X" and got the same distinctions.
The map in my Encyclopedia has the aq/bq border run straight through Earth.
Exact Time, GMT was needed by the British explorers to work out Longitude, and therefore cartography. A dinky village in Britain globally determined how maps were made.
If Humans charted the galaxy and made the maps the Humans used by the Federation, then of course Earth or the star it circles would be a concerning point in galactic astronavigation. Humans didn't. According to Enterprise, Humans got their maps from the Vulcans. Vulcan maps would centre on Vulcan, or at least Vulcan with respect to the centre of the galaxy.

As Earth became the seat of the Federation, and the Humans Joined the Federation, and the Vulcans joined the Federation, the star charts would be rewriten to reflect that shift in political power, which again would leave Earth bisected by the aq/bq border just like in my 22nd birthday present.
However...
The Universal Translator.
Everyone still uses their own maps, and the Universal Translator, makes everyone elses maps look like every one elseelses maps because everybugger is the same level of important.