Influence starbases should have double edge. They're there for the aliens to amuse themselves, and fall in line, but in yet they give no bonuses to the alien worlds. In the real world culural influence exertion generally brings wealth/ consumerism.
It would be much more interesting if the starbases helped morale and gave an economy boost to ALL the worlds in the influence. That way you may not mind so much getting influenced, as long as you can ride it out. It also would make them much less threatening.
Also it would make counter-influence stations more interesting. (they also benefit your planets) The bonuses would be fairly small, but significant such that you generally wouldn't build them just for your own planets.
