I believe that the art would could do without the auction house, however I also believe that the art world benefits exponentially from the auction houses, and without them, something new would have to take its place to fill the void. The Auction house has always been a somewhat corrupt place to buy and sell art, as seen through the auction houses' previous methods of bribing sellers through donating towards their favorite charities, and cutting commission rates before the price-fixing conspiracy. This price-fixing was only the latest in a chain of corruption.
Sotheby's and Christie's are two of the largest and most well-known auction houses in the world, and in the mid 90's neither were making enough money from sellers' commissions to keep their large art empires afloat, therefore they decided to enter a price-fixing pact, whereby each auction house would offer the same commission rate. FBI Investigations of the auction practices revealed that the two companies were in collusion. Both of the CEOs Diana Brooks, and Alfred Taubman were found guilty and were forced to step down from their positions. Taubman spend ten months in jail, and Brooks spent six months in home confinement. Both were charged a monetary penalty, and both auction houses were required to pay a total of about half a billion dollars together, to make up for the money taken from sellers.
One would think that after this huge conspiracy, people would be less inclined to use the auction houses to sell and purchase their art, and thus the companies would suffer, but this was not the case. In fact, the art market was not affected, both auction houses continued to prosper. The only people affected by this price-fixing, were the CEOs themselves, and the auction houses, but only in that they had to pay back the money that they had illegally received. It would make sense if people had lost their ability to trust the auction houses, and thus chose to sell their art pieces elsewhere, however this also was not the case.
I believe that people expect a certain percent of corruption from large businesses like these auction houses, and thus were willing to overlook this injustice because it was not surprising. Not only that, but I also believe that in the minds of some large art consumers, the idea of buying a piece at a world famous auction house increases the worth of the piece itself, and they would not trust the authenticity or worth of a piece of art were it not sold by one of these large auctions. This, coupled with the idea of an open auction where you are bidding against other avid art fans, provides the incentive to spend more money on a piece, and thus art auction houses have not been hurt by these charges of participating in illegalities.
Sotheby's and Christie's are also not alone in their corruption of selling art, many other world famous art auctions have followed suit and in 2010 France's most profitable auction site was also exposed, but for a different corruption. They had been housing an extensive art-trafficking ring. You can read more about this here:
http://www.nytimes.com/2010/04/27/world/europe/27paris.html
Although the art auction house is, by nature, a corrupt place, where the companies only care about themselves, and their profit, many people believe it is necessary to the art market, and I somewhat agree. It is necessary right now, because art enthusiasts regard it as the premiere place to purchase and sell art, thus it is believed that it gives the art bought and sold there, a higher quality, and thus a higher value. Eventually it would be wise, and doable to rid the art market of these auctions, however there would need to be another place to purchase and sell art with the same allure and prestige to take its place.