My thoughts around this are complicated by a couple things. First, I don't identify as a left-anarchist, and so I am not sure that I am the best qualified person to reflect on what an anarchist society of that sort might produce in terms of art, or the terms of distributing it. Also (and related) I am skeptical of the compatibility of civilization and current levels of technology with anarchy. Both certainly color the way I engage this question, though they don't actually have a whole lot to do directly with the things I am interested in looking at right now (so let me know if y'all feel like this is more a comment than an answer, I'll happily convert it).
Assuming a certain continued level of technology is available, I think it is quite likely films and music (and other art) will continue to be produced. The production, free from the constraints of capitalist civilization would, as I've touched on elsewhere, quite possibly look a lot different, but yeah. Of course people will go on making art in ways available and appealing to them.
I don't know that the internet makes the exposure to this art more viable - my experience of finding new art online is that there is too much. I have an extremely difficult time actually finding things that appeal to me beyond momentary diversion. Perhaps sans capitalism this would change, but I suspect that it is something intrinsic to the digitzation of art that creates a further level of alienation.
(An aside - Digitization is perhaps the wrong word here, but I am struggling to find the right one. I mean the removal of the art-object or spacial-art-experience. One easy example is music; I don't find myself able to seek out new music online and effectively digest whether it is something I appreciate. If it is music I already relate to via a live experience or physical artifact like a record, I seem to have less of a problem listening. The same holds true of books. I can not read digitized books. Without the tactile act of touching pages my mind doesn't stay engaged with the content of the "page.")
I think it is important to recognize that I am old enough that I did not grow up consuming art (or anything) online. I don't mean that in a "back in my day it was all better" way, but rather to acknowledge that I am of the generation where email and interwebs were introduced early enough that I am comfortable using them, but that I did not form my early understanding of interaction with anything remotely similar. This is probably significant to how much I hate engaging with art via the tubes. At the same time, I am also unconvinced that it is healthy for people to grow up with most of their interactions happening via text, web, and social media. This might change in a left-anarchy, I dunno. In my dream-anarchy whatever net remained would likely not be world-wide or 24/7, if it were at all.
I do think the removal of profit and bottom lines from movie making might quite improve the quality of output (though the devil on my shoulder is asking, "by whose standards?"), and the non-existence of the studio system would certainly free writers and directors creatively. I have some friends who are involved in independent film-making, and I think for folks on that level not a lot would change production-wise. ON the other hand, I doubt you'd see blockbusters any more (is the concept of a blockbuster even in any way translateable to an anarchic future?)
I am wondering about the part of your question about art being "pure." I don't really think there is such a thing as pure art, or that even in an anarchic society that the art created would be entirely free of constraint. We are human and as such there are lots of things that regulate emotional expression and content. Certainly we would be theoretically free to express whatever, but that is, to my thinking, an overly optimistic view of things once one starts to think about social mores and social pressures around conformity (things we would certainly still be fighting, but which would almost certainly still exist).