If common sense is not logical, what need is there for logical thinking?
It was explained above. Among the intellectual elite, particularly logicians and mathematicians, logic builds consensus and helps you avoid mistakes. The axioms act as a common anchor that the poindexters can unite behind. Logic of a non-technical sort, like political oratory advocated by Cicero ... ultimately is a play on words, because the axioms are too fuzzy. The first proper use of logic was Euclid. Logic used in politics by Aristotle or the Greek Stoics, failed in the face of Macedonian pikes.