First off, I miss the Asteroid Mining ships from Gal Civ II; and I'm hoping they'll return again in the near future. I'd rather pay once for a ship that can go out and get the job done than simply click on the asteroids, etc.
However, that's not the reason for creating this post. Yes, I do want them to return; but even so... What I'd like changed is to be able to assign asteroids that are within a Starbase's Area of Effect to that Starbase rather than a planet that is often far, far away.
Take it a step further and then assign the resources from those asteroids at that Starbase to a particular planet (via little shuttle ships or whatever).
In addition, one might also choose to assign them to a shipyard rather than the planet: those assigned to the planet support Social manufacturing; while those assigned to the shipyard augment ship construction.
SK
PS. When I first started playing GC II (years upon years ago), I was very surprised to discover that Mining Starbases weren't in charge of Asteroid Mining.