I've been thinking about this (rare, I know). And I wanted to see what other people think about Starbases.
Personally, I think that they have very limited uses, as, unlike base sins, they aren't strong enough to survive large fleets and the upgrades are so expensive early game (when starbases have an effect) that by the time you can use them it's too late and starbases get insta-killed by any mid-sized fleet.
I've found three "use" for starbases that are at least somewhat helpful:
-Stations to connect your trade routes through uninhabitable systems.
-Anti bomber support (upgrade weapons and put in the middle of a ODP fortress to protect them with AA guns)
-Fighter docks (pairs with above use) (fill fully upgraded hangers with fighters)
Also, the Covie starbase is even worse, as it pretty much commits suicide (it should have an upgrade so it's death explosion causes damage).