There are numerous other ways to approach it. For one, you can compete with free, and many do precisely that ( Cory Doctorow gives away digital copies of most of his work, but still makes his living mostly by and from his writing.) Another is to sell the associated scarcities rather than necessarily the copyright system itself (as Red Hat does).

And trying to produce it on a public basis produces problems in deciding what to fund. You run into this in public funding of science to, but there often are at least some public goals which helps guide this decision. It would be much more difficult to do with other forms of intellectual property (though we do in fact already do it to a limited degree, look at the National Endowment for the Arts).