Right place, right face, right time
He could act, like Elvis could sing, but he wasn't the greatest actor in the world, like Elvis wasn't the greatest singer. But Elvis had a few hits in key moments, when the world was crying for an idol, he filled a niche, so to speak. Dean was in a few key movies, Rebel without a Cause being the most important, the film expressed the feelings of a generation, another example of a niche that was filled.
And then their death, and the circumstances around it, did the rest.