Without cumbersome restraints that resist mental manipulations, humans are more likely to invent numerology than Calculus.

That is true which is why most people are not great thinkers. However high skill might not come from explicit reasoning, but from refining the pattern matching to prune away false branches. Mastery of a skill comes not from the ability to do a lot of Bayesian updates correctly and really fast, it comes from practicing till your intuition (=pattern-recognition engine) starts to reliably lead you towards good solutions and away from bad ones.