The HQ in career mode really doesn’t seem to serve much purpose. There are 3 things that are important that I’ve encountered:
- Where your pilot is located. You can pay to move around (at least in Freelancer mode, and it’s cheap) which unlocks more of the map.
- Where your aircraft is. This only matters in Freelancer mode. You can pay to move it.
- The areas you have unlocked. This matters more in Employee mode.
I haven’t found any evidence that the HQ location actually means much. You can just go elsewhere and you’ll stay there until you move again. Maybe I’m missing something but I think even when you have multiple aircraft and AI pilots, you can move the aircraft wherever you want.