Rather than "profoundness" I'd argue that there's something inherently beautiful about it. Granted, beauty is not a objective measure of anything in particular, and "we are like starstuff" might be an overly done cliche, but we humans are mostly driven by subjective and aesthetic notions, especially when we're young. If we taught more children that we are -really- like stars and how, with pictures and math they can grasp, we'd inspire more of them to get into science and technology, perhaps even bring spacefaring tech and the stars themselves a little closer to us in the long run.

Also, this validates cosmic brain memes.