More specifically, Back To The Future used a nuclear explosion to move Marty McFly around in time. To get back to 1985, Marty was actually supposed to move forward in time from a real life historical 1952 atomic test ... in a lead-lined refrigerator. It's an idea that still causes Steven Spielberg to wake up in cold sweats.
"Oh my god. I had a terrible nightmare. I put Harrison Ford in a fridge and then I ... oh no."
Recognizing the lunacy of showing how cool it was to climb in refrigerators in a movie targeted at least in part to children, as well as the absurd cost of mocking up an atomic test, the studio suggested they make the time machine more mobile and, well, not a giant radioactive explosion. Also, cruising in a magic science car is a little more charming than being propelled into your journey by nuclear horror. Boom (heh), instant icon.
Oh, and because it isn't just about the money: Doc Brown also had a pet chimpanzee as a buddy in the original script. The movie, one of the most famous comedies in American history, just didn't have enough ape reaction shots. How would people know that they were supposed to laugh if they didn't cut to a trained chimp comically slapping his forehead after each of Christopher Lloyd's hijinks?