There are other ways to make money

There are many other ways in which originators of media can make money even if they allow free distribution. First of all, they can regulate the commercial use of the works. That way, commercial entities (such as Music stores, online music download services, D.J.'s in charge-for-entrance parties and commercial radio stations) must pay them royalties.

Another financial option is to restrict derivation of the work. That way, persons who wish to build upon the work or include substantial parts of it in their own must consult the originator.

Another option (of less substance) is to require attribution for the originator. That way, people who wish to build upon a work without crediting the originator must purchase permission from him.

These three methods together give enough options for an artist to make money off his art, without restricting non-commercial copying.

This is naturally excluding live performances of artists of various sorts, like Rock concerts, that are also a huge potential source of revenue.