It will never be too late to get into the Harry Potter universe. I think that merit of the series/character is that it summons all the classic elements of fantasy, fables, myths, Bildungsroman, heroic fiction, children and adult fiction, religious and politics, detective and horror, in one single story masterfully crafted by a very clever storyteller.
I remember in 2001, when I started grad school at Ohio University, I was amused at the idea that Harry Potter had become part of the reading list, not only in lit courses, but in some social sciences.
The fact that it became such a massive commercial success speaks about effectiveness of Rowling's strategy at appealing to as many different audiences as possible.
My guess is that she invites us to take for granted the principles of mysticism. Going too deep into cause-effect and our role in bridging the spiritual and the material realities might have deviated our attention from more tangible things, which I think was her ultimate goal.
Fantasy is just an excuse to make us reflect about common issues we would not have thought about otherwise.
Those who grew up reading HP should go back to those books. They'll look anew.