An interesting discussion that really falls on how Market Failure is defined. It feels tautological though.
Market Failure is usually framed as a coordination problem, and usually it is expressed as failures in producing public goods. It also is framed as an issue of a free market because it lacks coordination (being anarchistic). David D Friedman has in his lectures shown that Market Failures occur in government as well and are essentially institutionalized. I've seen arguments that say government itself is Market Failure (manifest) that is creating government and have it produce things is an inefficient outcome.
My interpretation of this though is that part of that definition is that you are doing a comparison to some other possible economic state, that is some imaginary efficient outcome (the failure is in not reaching that). So someone could hold the perspective that the most realistic efficient outcome that could be imagined, given the conditions of individuals being separate and limited in sharing/conveying information to each other, and the latency of that information spreading and coordinating, would be an outcome achieved by a free market. And maybe that is what we should be comparing against.
Their argument though lands on the idea that there are 'entrepreneur failures' in free markets but not 'market failures'. Before there is an entrepreneur failure the entrepreneur believes they are on the right path and so they have efficiently allocated their resources towards that end.
I'm not sure I buy into that though from a tautological perspective, I can see how a free market can handle market failures, but it seems at least possible for there to still be coordination problems to solve in a free market. An example coordination problem would be that we are all exposed to information that "doctors make a lot of money", so we force our children to go to medical school, but when they graduate they discover they are competing with a lot of others and their income is significantly less. But if everything else were efficient this problem could be avoided. For example if there is a sudden increase in demand for medical schools, people would see higher prices to get into them and that would naturally reduce the number of doctors and doctor income would not be impacted as much, some doctors would possibly become teaches in new schools because schools have more money. Assuming those are naturally efficient and there are not coercions (government regulations, etc) distorting them.
As an example, Uber solves coordination problems (coordinating drivers and passengers/deliveries), and you would have Ubers in a free market solving these problems. I can see how you can say that when Uber didn't exist that there were no market failures because no one yet thought of the efficiency Uber would bring. But I don't think that tautology is useful to an entrepreneur who can see how we are presently inefficient (there are market failures) and how they can make us more efficient in the future through network/information technology. Sure in a tautological argument you can defend against those who want to use government to solve those problems, but it also goes against the entrepreneur!