I think the answer to your question is more psychological than military. There is just something deep rooted in the DNA of every Male that mkaes him want to be a great warrior.Some grow out of it and some dont. This was necessary for survival in ancient times and whether we realize it or not that need to be a protector of your tribe is still necessary today.
Im sure that in pre-historic times boys wanted to grow up to be like the biggest, badest cave man in thier tribe. Rambo just happens to be todays version of the ideal warrior. Unfortunatly Rambo is fictional. Thats why I wish that History was taken more seriously in todays schools. There are real life heroes that would be much better role models for todays future warriors but most kids never get a chance to hear about people like Audie Murphy, Sgt York, Chesty Puller, Nick Rowe, George Patton, and all of our Medal of Honor winners, but all of them have seen Rambo.
Anyway, thats just how things are and if things like Rambo, video games, and Rap music are what get kids motivated to serve their country then so be it. Once they arrive at Basic Training they figure out fiction from reality.