Spontaneous? No. Market economics developed over centuries or more. The problem is, they did develop as a natural outgrowth of human activity.
I think the trouble we (anarchists) run in to arguing with ancaps, etc. is that to some degree, markets (including "free markets" I suppose, that is a strange abstraction that needs a lot of dissection) are self-organized, inasmuch as they are organic in development. Capitalism as it exists now is highly controlled and regulated, but markets and economic exchange didn't develop thanks to a shady cabal of power-hungry men scheming to gain global control.
Like most things I hate (and most things I love) about humans, it developed over a long time, as humans made choices that seemed sensible? expedient? practical? in the moment. These choices developed from lots of other s/e/p choices made before them (most likely generations before). By the time we are talking about deeded ownership of property, monetary transactions, capital, and the rest, we are already so far down a path that it is, without stepping away, hard to conceive of other options, and when options are available, most people choose what seems most s/e/p in the moment.
This is one of the things I most appreciate about anarcho-primitivist explorations such as Zerzan's Origins essays ,or Against His-Story, Against Leviathan! by Fredy Perlman, is that they explore the roots of how we got to a place where things are so fucked, and they look at it as a series of decisions based on those that came before. Granted, JZ tends to become a bit dogmatic in his conclusions, but the asking and the probing of where all of it began is really helpful and important.
The thing is, markets might've developed organically. So does cancer in a body. Does that mean that one with a cancer just should embrace it as a welcome spontaneous or self-created part of themselves?