for other media, such as music, video and animation, one of the problems is that there is a barrier to creating casual content with decent production values. likewise, something like a play or a movie requires a longer-term and more coordinated effort than just someone sitting in their bedroom writing a story. but i believe that if the means of production were more accesssible, people would put in the effort for the sheer joy of creation. (doctorow's "pirate cinema" is a good read in that regard; the protagonist's art form was creating movies stitched together from clips of other movies. a true creative commons would make that a perfectly viable art form.)
note that history has plenty of examples of really good writers and painters dying in poverty. they were moved to keep creating nonetheless; it's a very powerful human drive.
the one bleak aspect to all of this is that the ability to produce art for free is biased towards people who already have another means of support, and one that leaves them both comfortably-well-off and with free time and energy. yet another way in which a basic income would enrich the world.
edit: i also feel that money-as-a-reward has a deeper problem than the fact that it's currently shackled to ads. once you bring in money (and the implicit idea that the better and more popular your work is, the more money you'll make from it), your incentive is to impose access controls on it, because if there's a way to access something either by paying for it or for free, most people will go the free route. that adds an antagonistic note to the relationship between the producer and the consumer, as well as triggering a spiral of overreach with respect to "intellectual property rights".
That is not always true. Highly specialized content, which has tiny audience, can be equally profitable. In the end, money reflects the need for the content.
it's also possible that the desire to have everything be free will trigger a worse-is-better downslide where no one creates really good content because no one will pay for it because everyone is satisfied with good-enough free content, but i doubt that will happen; i just want there to be enough good-enough free content that people who can't or won't pay still have their needs met.
while we're dreaming, there are two things i'd really like to see emerge:
1. a true shared culture with a continuous gradient from pure consumer to prolific producer. something like tumblr is a good proto-example - there are people who just browse feeds, and people who reshare, and remix, and add their own writing, and write entirely new posts, and every now and then a truly beautiful post emerges and makes its way out onto the wider web
2. a thriving distributed patronage model, where people fund the creation of a work via kickstarter etc., but then the work is released freely, having made its money already
both these things are already starting to be experimented with, but they are badly in need of mindshare.