It seems odd that influence starbases produce influence where there are no people, such when their influence radius includes only empty space or uninhabitable planets. Sure, we are producing lots of music, propaganda, and neat clothes -- but there is simply no one there to consume it. Either influence starbases act globally (and hence there is no reason for them having an 8-hex radius) or they are really odd.
(In addition to being way too powerful -- defend your starbases well and a cultural victory is simply way too easy on any setting compared to any other type of victory.)