Why were Mozart and Beethoven known as concert pianists as well as composers?

Wolfgang Amadeus Mozart and Ludwig van Beethoven were renowned as concert pianists before they achieved their fame as composers because their careers were built upon their exceptional abilities as performers in an era when the "concert artist" was rising to prominence.1

For both men, the piano was central to their professional lives and public identity:

• Mozart: He famously described Vienna as "the land of the piano," and his greatest triumphs in the city were as a pianist-composer. He frequently performed his own works and improvisations at public concerts, often conducting his symphonies from the keyboard as well. His piano concertos served as the primary vehicle for his concert activity, allowing him to showcase his virtuosity and melodic ingenuity.2
• Beethoven: Before moving to Vienna, Beethoven had already established a significant reputation in Germany as a piano virtuoso, particularly noted for his talent for extemporization, which some accounts suggest surpassed even Mozart’s. His early success in Vienna was driven by his ability to move audiences to tears through his playing, which secured him the support of the aristocracy. He frequently performed his own concertos in public, which helped spread his fame internationally.3