STARBASES

Yeah, I think there is a lot that could be done with them. They could reduce the time it takes to travel along any star lane they are connected to for example (resupply) which again presents interesting strategical choices. 

Similarly they could provide a boost to border growth helping you to nab some of the stars/black holes etc that provide bonuses to your systems.

They could assist with repairing your fleets. Provide diplomatic/economic/scientific bonuses. 

have entire techs and a new class of weaponry available to them, have unique battlecards and most importantly

look cool as a cool thing.  

There really is a lot of scope for them. 

They could also be a alternative to planet colonization when you desire to take controle of a system.

At a certain point, due to the overcolonization penalty, you are forced to ignore many star-systems. Adding Starbase could be an alternative, with the possibilty of adding luxury/strategic ressources exploitations, Dust collecting or Science labs modules, allowing to specialize your Starbase to the system.

The starbase could also be a defensive asset in case of attack, and could be like a fixed unit during a space battle, with it's own weapons (following the Deep Space 9 concept above)

It is important thougth that a starbase should never be fully equal to planet colonisation in terms of exploitation, or be military too stong, as repelling large fleet should require the assistance of a defensive fleet.