I used to get those as well as a kid. The technique, nightmare-within-nightmare was a trope of 80s horror movies and that's where we got it (incepted?) I believe :)

On the movie, I think the really interesting part was not the recursive dreaming but rather how our ideas- that we think are novel - are not actually ours. After watching it, me and my wife started observing it on each other. Me or she would come up with something and the other would point out some conversation in the recent past that seeded it. Fun and a bit scary.