In fact, a fairly important figure in "neoliberal" thought is Hayek. Hayek (and Hayekians) argue that not only is the economy difficult to quantify and describe formally, it is impossible. In his frameworks price and choice are conveyors for knowledge.
I would even say that the most serious hubris in this vein has been the Stalinist and Maoist "5 year plan" which aimed to quantify economies in accounting terms.
As for Hayek, I don't think he is unique in the view that price is about knowledge. While Hayek was the more readable and reasonable one between him and Von Mises, I'm aware the Austrians don't really believe one can scientifically study the economy, but I also think there is plenty of evidence that has refuted this: we can quantify and describe a large subset of the economy with predictive power.
The question for society is , does this even really matter? We never used to subject ourselves to economics and markets as the totalizing sphere of human achievement, it was one of several areas of social organization alongside community, politics, family, religion, etc. We only start caring about this stuff when we want to compute dubious universal ultility functions and the like.