Seriously, the idea of a free market is as absurd as communism. In both cases, I want to know what actual, concrete, real-world evidence points to even the hint of the possibility of the theory.

The "free market" relies on assumptions that usually aren't true in practice. The lack of colluding parties is the most notable. The difference is that under "capitalism" the colluding parties are a bug (albeit one that no one with any power wants to fix) and under communism they're a feature. I don't want to venture into No True Scotsman territory but there's a lot of awful shit going on, and rooting that out would the market more "free".