| doesn't an influence base always add to your overall empire's influence |
Actually, no - an influence starbase only raises your influence level within its 8-parsec effectiveness radius. I can't point to any recent posts about this, but it's been debated before. Once I've flipped every planet within that radius, I immediately destroy influence bases so that I can build the next one more cheaply - unless it is also holding back another empire's influence in that area.
Getting to the original idea of "starbase creep", though, I have to say that this is one of a few good, solid ideas for enhancing the game experience that I've been following lately. Rather than looking for a way around the proposed speed change, mobile starbases takes a different tack that could measurably enhance the power of slower-moving fleet; particularly on the defense, which really needs some help.
It would also breathe new life into starbase-related strategies. I honestly can't remember the last time I built a military starbase. This is in small part from constructor micromanagement fatigue, but mostly because they get left behind too quickly for their starship enhancement modules to have an effect on the game that merits their high cost. Even as an evil faction there is a high opportunity cost to military starbases, as they consume time and resources that I feel are better used on warships.
If it were implemented, I'm sure it would be as a starbase module. I think having space tugs to pull starbases would be extremely cool, but it sounds like a lot of extra coding and may not be something the AI could handle well. That would be the biggest obstacle I can see, actually - can the AI be 'taught' to make good use of a starbase that can be moved?