I mean when you think about it, most people would be more familiar with TV and movies than mythology so referencing that would be more common than recounting which time Zeus cheated on his wife. A weird thing about Star Trek is how people generally experience classical entertainment (Shakespeare plays, classical music) while modern(ish) and futuristic stuff (from our perspective) doesn't really happen. Off the top of my head, there's Riker's jazz, Tom Paris' 50's fixation, and O'Brian singing Louie Louie. I guess people won't remember the 20th and 21st centuries very well.
Irenicus, his celibacy involuntary.
But then I'd have to watch 1 and 2.