unless they're a faceless-threat type element like the Borg
How can you not identify with the Borg? Are you not on Facebook?
You could take any of the alien characters who represent aspects of the human psyche, invest them with more complexity
I read this as "make them fully human". In which case, what is the point? To me, if we were going to have an alien captain, part of the point would be to examine exactly how their very alienness, culture, and biology play into things - not to just have them be a human in knobby-headed makeup.
We might watch that (either way, honestly

), but I just don't think it would fly for a general audience.