That’s an excellent point. In the first third of the 1900s, sheet music was a major industry, and broadcast/recorded music was a minor afterthought. Indeed, as “player pianos” and similar automated music production became more common, the paper rolls were treated as just another form of sheet music.
Even today, it is the writer of a song, or the composer of the music who hold the copyright and gets the royalties. With infrequent negotiated exceptions, the band that you associate with a favorite song earns almost all of its revenue from concerts and other live appearances, not for their gold records. In the late 90s, the RIAA lobbied hard to have all recorded music presumptively classed as “work for hire” (meaning: “I hired those guys to play the music for my recording, therefore it belongs to me, not to them”)
Indeed, recording contracts typical of this “consumer music era” often effectively indenture bands to the label–a moderately successful album actually leaves them owing the label money “after expenses.” This is the root of many famous incidents in music, from the Beatles recording their own music on a four-track and releasing it through their own label, to The Artist Formerly Known as Prince" (He successfully argued that the contract only covered performances of “Prince” -a music act- and not all work of the person Prince Rogers Nelson, thereby freeing himself to pursue music that didn’t meet the label’s wishes, at the cost of the right to use the name under which he had become famous–until such time as the contract expired).