Stellar Mapping and Coordinates
The reason why we centre our galactic coordinates on the sun is that is where we are.

What actually is the purpose of a coordinate system‽ I'd like to be able to point to a body and say that it is at coordinates X, Y, Z (with uncertainties in each direction)

Now we know the direction of the centre of the galaxy, but we don't know it's distance with accuracy. If we were to use the location of the centre of the galaxy for the galactic coordinates we could not give accurate coordinates for any of the local stellar objects. 

If we had a warp drive and could travel halfway across the galaxy before lunch then it might make sense to use a different set of coordinates. However, as things stand there is nothing wrong with being Earth centric.

I have mentioned the remainder of the question in comments.