Burning Man and the free software movement don’t have a standard money economy. Instead, they have what’s known as a gift economy – everyone makes goods and services, and then gives them away for free. People get social status in proportion to their gifts, with more impressive gifts being awarded higher status. Hence, people are incentivized to make things other people want, and workers can specialize and use economies of scale during production, just like a monetary economy.
Where gift economies excel is in providing public goods. A public good is something that a) you can’t stop people from using, once it’s been made, and b) is infinitely copiable, so that one person using it doesn’t stop other people from using it. Radio broadcasts are an example. You can’t really charge for a public good, because people can get it whether they pay or not – there’s no incentive to fork over the cash. Hence, public goods must be provided by a gift economy, or by another non-conventional economy, like by the government taxing everyone and building roads with the tax money.
Interestingly, the rise of mass production has allowed the music (and more generally entertainment) industries to shift from a money economy to a gift-based economy. Before recorded sound, music had to be heard in concerts, and concerts could be charged for. You could take the fifty dollars from a concert ticket, and pay one dollar to the bassoonists, one to the clarinetists, one to the flutists, one to the percussion, and so on. However, the sounds from these instruments are essentially wholesale goods, not retail goods. No one wants to hear a single clarinet or a single drum by itself – they care about the sound of the whole symphony.
The infinite replicability of music (through phonographs, radio, CDs, and now the Internet) has now made music more and more of a public good, and this economic shift has gradually eliminated musical wholesale goods, in favor of retail goods. There are no symphonies with a hundred people anymore; bands are small, and I think their size is limited by the need to have the sound of each member be a significant contribution to the overall sound, making it a retail good and therefore gift-able. During the CD era, there was at least some money in music, but the salaries paid to musicians were very low in comparison to their level of talent and hours worked – the main compensation was the social status they got as a “rock star”. With the Internet, even small amounts of money are going away, and musicians are rapidly becoming hobbyists who give their products away on YouTube.
One of the reasons there isn’t much of a job market for painters is that paintings are now also effectively public goods. Once a work has been painted, you can produce a near-perfect replica at very little cost – everyone can hang a copy of the Mona Lisa on their wall. If you made a modern-day Mona Lisa and tried to sell copies, it might get upvoted a lot on Reddit, but it wouldn’t sell very well. Places like Burning Man have really good art, because the gift economy creates a type of good you’d never see in the normal American economy. A really good artist can’t get rich by selling copies of their sculpture… but they can make copies, give them away, and then enjoy high social status from all the people they gave them away to.
However, to explain why a gift economy won’t work for most situations, we have to also distinguish between the two main types of non-public goods, retail and wholesale. A retail good is one that a buyer will find useful directly, while a wholesale good is used in the process of making a retail good. The vast majority of America’s economy makes wholesale goods that most people don’t even know exist. A depleted uranium aircraft counterweight is useful indirectly, because it makes flying cheaper… but you can’t even buy them as a consumer, because they don’t have any direct use (other than to chemists with odd hobbies).
In any even vaguely modern economy, there are lots of complex interdependencies, with lots of intermediate wholesale goods. A piece of art at Burning Man is made from many different parts, but it isn’t made from parts found at Burning Man – it’s made from parts produced by the money-based American economy. Burning Man has lots of art that gets presented as a finished product, but it doesn’t include the wholesale chain of the bolt to hold together the oil rig to pump the gas to drive the truck to cut down the tree to provide the wood to nail together into a sculpture. Art made only from wholesale goods available at Burning Man wouldn’t be very impressive.
In a gift economy, how highly incentivized a good is (and, therefore, how much gets made) depends on how many people consume it, and how highly those people value its consumption. Hence, wholesale goods can never compete with retail goods, because the market for a wholesale good is so much smaller. If twenty Burners make sculptures that need a particular kind of nail, they are each incentivized by the desire to show off to fifty thousand people. However, if someone were thinking about bringing nails, they would only be able to show off to twenty people. As the obvious consequence, everyone builds sculptures and no one tries to bring nails, and so the gift economy falls apart without a larger monetary economy outside to support it.
The Rationalist Conspiracy 
Ah, but the 20 people who would appreciate the nails would be high-status people. Earning the appreciation of high status people (and having that appreciation be made public knowledge) should increase one’s own status more than would earning the appreciation of the same number of medium status people. Presumably, this effect isn’t enough though or else we would see more guitar maker-donors who are themselves the social equivalent of rock stars.
There are no symphonies with a hundred people anymore
You make a lot of good points, but this statement is about as wrong as it gets. There are probably more “symphonies with a hundred people” now than there have ever been in history. (Every major city has at least one.)
In fact, what there probably isn’t as much of as there used to be is private performance. Due to the availability of recordings, as well as the proliferation of local professional ensembles, people no longer play music themselves (as much as they used to); instead, they listen to other people playing it.
That’s obviously silly – it doesn’t take into account number of symphony performances per capita, or per unit of GDP. In absolute terms, there are more slaves now than at any point in human history. Yet, I wouldn’t hesitate to say “there are no slaves anymore”, because the slave population is such a tiny *fraction* of the *total* population.
Number of symphony performances per capita is also surely at an all-time high. Only a small fraction of the population would have even heard of the concept of a “symphony performance” prior to mass media.
GDP I’m less sure about, because GDP was so miniscule in the old days compared to now.
As you surely know, not everyone would regard it as obvious that the slave population now is insignificant compared to the past, simply because it is smaller in percentage terms. At the very least, it isn’t “obviously silly” to assign significance to absolute numbers, whether of slaves or symphonies.