I think the first problem with that line of thinking is the assumption that the market needs to always be right in order to advocate it. The market simply reflects what people want and are willing to pay other people in order to get. The argument in favor of markets is that the price system communicates the desire for certain products in a very clear way that creates an incentive for other people to provide for those desires. A classic essay on this is F.A. Hayek’s “The Use of Knowledge in Society,” which you can find online for free. Basically, the argument that Austrians have historically relied on is that central planners face serious problems in being able to know how best to provide for what people want, and the signals communicated by the price system create a structure of incentives that often has the capacity to bring about better solutions (by everyone’s standards) than could be implemented through government action, through the decentralized actions of market actors. This argument is augmented by the Public Choice school of economic thought, which points out that when we acknowledge that government agents have their own personal motivations for action, and so can be prone to acting outside of the public interest, the picture becomes even more grim for government’s ability to solve problems. So when we talk about the market being desirable, what we have in mind is that central planning is generally not the best tool for solving social problems and addressing the needs and wants of the people, and the market has a really great track record with these sorts of things.
But just like how the market chooses Britney Spears over Pink Floyd, we can’t necessarily offer any defense of market outcomes besides that they reflect what people actually want. So far as people, for whatever reason, do not understand that Britney Spears makes really crappy music, they will demand to listen to her, even though I personally think they’re stupid on that account. In the same way, most people really do think that the economics practiced by the mainstream is the best way to go about things, and the market seems to reflect that perfectly. And surely, I would love to see people making better choices, because I think that they would be much happier if they did.
This, however, is where the libertarian in most of us speaks up, and points out that if people didn’t try to force their opinions on each other all the time, none of this would really be an issue. Objecting to market outcomes would be, essentially, like me saying that I hate the world because Britney Spears is more popular than she deserves to be. Maybe that’s true, but it’s not really important. That’s because Britney Spears fans don’t force me to give up listening to Pink Floyd, and I have no interest in forcing them to stop listening to Britney. But in an important sense, mainstream economists force their views upon us all when they come out in favor of government policies which Austrian economists believe to be misguided and ill-advised. So it becomes really important for us to try to go out and convince people that we’re right about this stuff.
Notice, that has nothing to do with the market itself; that has to do with the fact that the political order of a society is inextricably tied to the dominant paradigm in that society, and insofar as today’s mainstream economists are generally accepted as being correct, our political order will reflect their ideas. That’s why the LvMI is working hard to change people’s minds, and to educate people about what’s right.
It occurs to me, though, after writing all of that, that your question was likely addressed to the idea of a “marketplace of ideas” which is a metaphor (not a very good one) which has absolutely nothing to do with the Austrian advocacy of the free market. If someone objects to free economic markets on the grounds that free economic markets are not supported by the dominant ideas within the “marketplace of ideas,” then you have my permission to smack them across the face and tell them to go learn some economics. And for good measure, have them go learn about communication theory and social psychology.