instance build a shrine on the Main World that would increase morale, try to convert planets to your beliefs, lead holy wars, Jihad (the Krynn are kinda doing that already I think), wrath of God that would wipe entire systems, Armageddon clock (Win within X turns or the entire galaxy is destroyed) and why not summon deities to give certains civs the edge in battles..and ultimately add a Religious or Ideological Victory condition.
Actually it has a minor advantage, fictitious religions can have stats, can be differentiated, real ones can't because of political correctness. And you are forgetting that we have customizable races. Just make the terran religion neutral by default with no stats, unlike the "alien" religions. There would be seven graphical representations for human religions (the same as in civ4) and their corresponding names, you would be able to customize the "human" religion. The AI would just pick one of the 7 pre-prepared symbols and the proper name. Alien religions would have default stats and symbols but could be customized as well.
The real question is what religions would add.
Divine power are too much and not appropriate for a SF setting, let’s just assume that all of the gods are make-believe. A scenario is another thing. It could add a twist to diplomacy… evil Dregin in Christianity may be on good terms with neutral human Christianity or be at odds with good human Christianity in another game. Making the appropriate (depending on you’re relationship) increases or drops in you’re approval and you’re relationship with the other races. Maybe the evil humans adopt the Dregin religion? Claiming that they and the Dregina are sister races, starting a crusade event. Or perhaps the Yor after centuries of atheism, find an interest in Buddhism or a Torian religion.
Some cool Mega.events could be added. Like: Powerful beings invade the galaxy, calming they are well, Gods. Funding a religion that gives them more and more power as they forcibly convert more sentient.
If a deeper government system (ala civ or even EU3) was ever implemented this could allow official state religions.