Wasn't Einstein motivated to develop Relativity because he was obsessed with the idea of travelling on a light beam?
Honestly, I don't know. Perhaps he wondered about what it might be like to travel on a light beam, but I doubt he ever thought it would be physically possible to "ride" on a light beam.
More to the point, the data existed first: the Michaelson-Morley experiment showed that something was wrong with classical physics, and suggested that the speed with which light propagated was invariant regardless of the observer's frame of reference. This is the basic premise of Einstien's Special Relativity: that light travels at the same speed as measured by all observers, regardless of their frame of reference. Starting from this premise, which was suggested by experimental data, Einstein then followed it to the logical conclusion, which was Special Relativity.