> remember that the great classical composers were the rock stars of their day.
I don't have a source for this but I hear it a lot and I strongly suspect it is a historiographical myth. Pretty much only a very small minority urban (relative) elite had access to live professionally performed classical music during most periods when it was being composed. This is also the group whose writings form most of our current knowledge base about these periods, and whose writings are of course focused primarily on their own interests. We can't really see what they didn't see, or didn't care enough to write about.
But contemporaneous with this elite music there were european folk music traditions, taught and performed ad hoc by individuals or small ensembles in homes and gathering places of the vast majority of "normal" people (peasant farmers, later urban laborers), and including some traveling performers who were known by reputation.
So yeah the great classical composers were wildly popular among the people who listened to the kind of music that they composed, but that was an extremely small part of the population. We don't have very much information at all about what was going on musically with the greater part of the population, but it appears to have been a completely separate thing, it's doubtful the great composers had any name recognition among the vast peasant masses.