Contemporary art, be it music, movies, games or paintings document the history of culture and society. There's no such thing as "enough art", because there's never any "future art" already made. For example the types of games made document well the advances in technology and changes in society in the visuals, themes and plots they involve. None of those games could've captured the zeitgeist as well as they all combined have. In addition, no game made in the past reflects present, and as such cannot be a commentary on it. One could argue most "art" created doesn't deserve the title and from an art standpoint I'd agree, but even those document what was sold, listened to and considered something people like at the time it was released.
Furthermore, there's still novel art being made. I believe the world is a nicer place with, for example, some of the recent-ish games like braid, the bridge and undertale. I do love many older games, like earthbound, but there's only so many that actually do anything thought-provoking. Sure, if I defined "entertained" as "consuming entertainment" I could just slap youtube on autoplay today and probably never see the same video twice, but I do not think I'd enjoy myself for long. The specific content of the entertainment matters, not just the quantity.
The problem is that there's no telling how much culture needs to be produced for those few gems to appear. They may be the product of someone being inspired by a single line said in a paint-by-numbers first person shooter at a specific point, which provoked a thought in the future developer's mind. The best way to produce more good art is to provide a fertile soil to produce more art. Of course, this should be balanced with other needs of society and the current copyright regimen is way out of line, but new art isn't worthless.
As I said, there will always be some culture still produced. In the UK, for example, we have (and have had for a long while): the BBC (public broadcaster, paid for by a special tax on televisions -- likely soon to be internet as well), the Arts Council (funded by general taxation and lotery grants, itself funds opera, theatre art galleries and classical music etc.), advertising-funded TV, FOSS games, YouTube etc.. Any combination of these could replace what is "lost" (or "purged"
) by copyright abolition. Perhaps production values would not be so high, but the BBC's output suggests otherwise. Or people may read more books, as those are comparatively cheap to produce.
Despite that, I dispute that new "art" (a least professionally-produced music, games and video) is so important -- particularly in its current quantity. People have other things to to (at worst, those suffering withdrawal could take up amateur dramatics). Documentation of culture and society is well served by those trashy cat videos and celebrity gossip and such; historians of the future shall have no trouble (assuming the data is preserved well). Indeed, a sudden decline in certain types of music, video and computer games would give the historians a lot of stuff to talk about (and such a decline would, indeed, demonstrate some important tendencies of our society, not least the relative value of different aspects of culture). For "contemporary commentary", which generally does not remain relevant for very long (and, so, for which copyright protection has little value), such as topical comedy and news, well, we have enough without more permanent types and copyright will hardly affect it.
Perhaps my view is skewed, though, as I hardly ever bother with new "art". I generally only bother with things that I have observed people discussing for years since their releases. As such, I have hardly ever experienced any "zeitgeist" from a film or music. Games are a little different, as the graphics changed so much in the period from 1988 to 2008 (I play few games released before 1988, so far) and then stagnated, but I would hardly call that "zeitgeist".
A final note: in our current system, a huge amount of stuff is produced, and then effectively discarded, and a small proportion of it is considered brilliant. In a system with free modification of everything, fewer things might be produced, but with more variations of them and with overall improvement over time. Xonotic, for instance, is not the same now as it was (as Nexuiz?) 10 years ago, but the important things are unchanged. In 10 years it may be even slicker (on a desktop computer, assuming they do not (stupidly) try to change the interface to accommodate other devices, like the soon-to-be-super-successful Pyra). Imagine what a little state funding would do to all these FOSS games?