I think there's also an element of universality to these stories, which their fantastical settings allow to shine through more than a show grounded in a specific time/place. The Lion King is about family struggles, power and envy, guilt, and trying to find one's place in the world. Wicked is about feeling different, being let down and becoming stronger for it, and the extraordinary power of friendship. Anyone can relate to something there- anyone who has lost a loved one feels Simba's desperation to see Mufasa's ghost, anyone who has ever felt different or not good enough can feel Elphaba's growing isolation. You don't have to understand the politics and culture of a specific time and place- as much as knowing Bush-era politics might enhance Wicked, for instance, it's not crucial to the story as a whole.
As for Phantom, well, not sure what's as universal there. Maybe more people than we thought have dealt with stalkers who imply they're a dead parent? :P