Eric, my old roommate and a very talented composer, asked me if there's a good economic reason why so many arts organizations choose to register as non-profits, and whether that implicit government support is justified.
Let's take broadcast television (PBS) as an example. This applies very easily to things like public radio (NPR), and it shouldn't be hard to abstract to more general arts applications.
There are a number of specific principles that affect goods whose use is determined by creative popularity (as opposed to usefulness). Firstly, no two creative goods are the same, and, theoretically, an infinite number of number of different possibilities exist for the structure of creative goods. One can find close substitutes to a creative good, but these substitutes are imperfect.
This brings us to the second principle. The variety in goods means that it can be very difficult to predict the commercial success of artistic goods, meaning that market sizing isn't easy to do, except by using analogous, previously released creative goods. The more unique the creative good, the fewer analogues, meaning that the successes or failures of really unique goods are really hard to predict.
Thirdly, most creative industries are very, very high fixed cost and low marginal cost. The marginal cost of broadcast television is zero; the fixed costs throughout the industry of designing the program and then broadcasting it are very high. Live performance art also has low marginal cost (each additional viewer doesn't cost any more, up to capacity of the theater, and it can be run over and over again to minimize the costs of the capacity constraints), but high fixed costs (hiring actors, writing a script, putting together the performance, etc). Even books are often high fixed and low marginal cost - the paper and binding for a book is very low compared to the effort required to write and edit a book, which is why something like 80% of books lose money.
If creative industries were less capital-intensive, the first two conditions would be less important, because you could diversify your risk away with lots and lots of productions. However, if you have a budget, you can't triple build expensive capacity to try three different shows at the same time. You have to guess what will work, and bet on it.
A fourth condition is that a lot of art has positive externalities. Material is often educational, and teaches people to behave better and be more productive. It can be informational, allowing people to know about world events and support more capable government and less waste. Some productions may make otherwise inaccessible form of art, culture or entertainment available to the general population, providing meaning and thus a nebulous form of utility not just to themselves, but the people around them.
However, because the arts market has high fixed costs (and thus barriers to many forms of entry), a for-profit-dominated art marketplace would mean that not every consumer is able to find art that maximizes productivity or utility. Imagine a world with 5 risk-neutral broadcast networks, where 85 percent of people prefer news, and 15 percent of people prefer cooking shows. Networks are paid based on number of viewers. If each network's expected market share is equal, then all five networks would choose to air news, with an expected draw of 17% of the audience. If high fixed cost prevents new entry, then the 15% of people who prefer cooking shows would not be able to view their cooking show, even though it's clearly an inefficient societal allocation (the opportunity cost of any other news show is any one of the other four news shows, which probably isn't a huge difference, whereas cooking shows are very different from news shows).
This is far more acute in areas where you can't charge based on preference, like broadcast TV and radio. Thus, shows like NCIS and Criminal Minds are hits, where everyone likes them just a little bit better than the competing offerings. Shows like Chuck and Friday Night Lights, whose fans love them a lot more than any other show on tv, but can't pay more to see them and keep them on the air, are commercial flops. This is easier to manage with books and live performance, and somewhere in the middle for packages like cable networks. One can imagine in the previous example, if fans of cooking shows are willing to pay X for the ability to watch a cooking show instead of a news show, and if fans of news are willing to pay Y for the ability to watch their favorite news show instead of their second favorite news show, that X would be significantly greater than Y, but the networks can't charge anything, so there is no cooking show.
This is worsened by the fact that it's a lot easier for producers to understand whether a creative good will be successful based on what is already available. Even if CSI lovers never needed an eighth crime show, they got them, because it's easier to look and say "Hey, CSI, CSI:Miami, CSI:NY, NCIS, Criminal Minds, Numbers, Law and Order and Law and Order: SVU are hits.... thus, NCIS:LA will be a hit!" Doing something really innovative, like Lost, Kings or Friday Night Lights (seriously, the first season of FNL is the single best season of TV I've ever seen) is a big risk that can flop. Kings was a massive flop, FNL was a moderate flop, and Lost was a megahit. The risks almost aren't worth it - look at NBC, who consistently have the most innovative lineup but the worst viewership, and thus profit, numbers.
I go through all of this to demonstrate that a for-profit system in the arts can run into serious problems if a variety of available products is important, which it is. Combine this with the fact that advertisers, who are a decent proportion of profits for many arts categories, prefer certain demographics to others (they tend to hate poor people, rural people and old people, for example, cuz they won't spend enough), and you have a recipe for some seriously underserved arts populations.
There's also an issue of calendar year. Performance and broadcast/cable radio and TV are often scheduled at the same times, to access periods during which audiences will be biggest. People who want creative goods around Christmas, or during the summer, will be underserved, as well.
However, a nonprofit benefits from a significantly improved cost structure (US corporate tax rates are 35%) and a mandate to create variation in the marketplace, instead of profit maximization. As a result, they can stay solvent producing types of art that a for-profit company couldn't, and they can target populations who need it and can't afford expensive substitutes (poor children, for example - look at all of the good that Sesame Street has done in its long run). They can air their products whenever they feel it's most needed. In other words, they provide a flexibility to the marketplace that wouldn't exist if all arts entities were for-profit.
Thus, there's a pretty good reason why artists, who often care as much about art for art's sake as they do about commercial success, would want to use non-profits as a vehicle, and why the government should be perfectly happy to let them do so in a budget-unconstrained policy environment. (We must ignore opportunity costs of government funds. For obvious reasons, that is a highly complex and subjective analysis and there is nobody alive who can possibly know the answers with certainty if there are government budget constraints).
(This post is adapted from a small piece of a paper I wrote for an Economics seminar during my sophomore year at Harvard, which examined public television in the US and made suggestions for improving its efficiency and impact. For those interested in this topic, I highly recommend Richard Caves' "Creative Industries".)