And hugging the edge of the galaxy like that there are not a lot of stars, which means not a lot of civilization so not a lot of people to trade with or restock supplies off. Any route chosen to the Bajoran Wormhole would not be a straight line. It would be a huge half moon arc smilie face dipping in towards where people are, and then back out towards the boon docks where the dominion wormhole is.
No Starship is an island.
According to that map half of Earth is always in the beta quadrant.
The planet is revolving.
But then it's the sun which is the centre of the sol system, so Earth is in the alpha quadrant the one half of the year, and in the Beta the other half.
Considering where Romulus and Qn'oS are, they didn't have much choice but in which direction to build their empire, even if most of it was just assimilating the old Vulcan Empire.