I think you're giving Mozart a little bit too little credit when you just say he was a classical music composer. You have to consider how much he wrote in just such a little time. He was very much a prodigy, or a "wunderkind" if you will. What Mozart did and had was this novelty and innovativeness around him. And also, he had a cult of popularity around him which only music stars in the second half of the 20th century would have, and like quite a few of them, he died young and this definitely added to the popularity of his works.
Another person I would add somewhere down on the list, by the way, would be Gregor Mendel for his contributions to genetics.