Other than being a neutral space that is safe from bombardment, does the Galactic Council serve any purpose?

Nope.

None other than the fact that there is a secret win condition tied to it. I think it reads "I win if I have more forces in the Galactic Council than any other player." or something to that effect. That and the obvious strategic positioning as you should be able to reach almost any other place from there in one move.

Though, with a game where movement is defined by two characteristics - you cannot block others from moving through a territory you control and that you cannot move more than 2 spaces (unless you play the Federation or control a Spaceport) - the central location becomes very important.

Making it a forced neutral space makes it an important staging ground for deploying your forces.