Financial incentives don't encourage great art, they only incentivize commercial art. There are overlaps, but we can't pretend those are both the same thing.I don't entirely agree. Appreciation of art is subjective by nature, but the way we usually quantify value in our society is financial. A work that is popular will be more financially successful. A work that does not have such broad appeal but which is worth a great deal to a smaller group can also be successful. So unless you want to make some argument that art that is neither widely appreciated nor strongly appreciated by a few can still be great, I don't think the concepts you mentioned are as independent as you're suggesting.
I would also point out that copyright incentivizes the creation and distribution of utilitarian creative works, not just artistic ones. In some respects this is the more valuable side of copyright, because as you point out, with artistic work there will probably always be some level of creativity whether or not it's compensated. With more practical works, say business accounting software or a high school science textbook, there's much less incentive to create the works without some form of money or other compensation involved.
But even in the case of artistic work, I think it's fair to say that a successful professionally edited and published novel is likely to be better writing on average than most popular fan fiction. There are some impressive amateur video productions on YouTube these days, but no-one is making a hobby show with the production values of Game of Thrones. A few potentially decent games have achieved quite impressive funding through Kickstarter, but some of them still haven't actually been shipped years later, and typically they're multiple orders of magnitude below what the budget for a modern AAA title.
You can draw similar comparisons in most fields covered by copyright, whether artistic or simply utilitarian. Certainly not all commercially produced works backed by copyright are successful. Copyright doesn't guarantee anyone a financial return on their hard work. However, it does provide a direct incentive to produce better works and distribute them more widely, because the more successful a work is, the greater the return it will generate.
The only two fields I can immediately think of where serious money is made from creative works but probably would still be made if those works weren't subject to copyright are live performances and software created to support something else rather than for sale in its own right. Even then, not everyone protected by copyrights would necessarily benefit; for example, a band or orchestra might bring in a lot of money for a live concert, but probably someone else wrote the music or songs. So again, the financial incentive to write the best music comes from wanting as many performances of that music as possible to be enjoyed, and thus to maximise the royalties.