Given how wealthy and populous the Free Cities are, why do they rely so much on mercenaries? A loyal and professional army would be more reliable and effective than anything except the Golden Company. With how often Myr, Lys, and Tyrosh fight each other, I’d think they would be eager to gain any advantage over the others. Or Volantis in the days when the tiger faction ruled.

When it doubt, go back to the source….

The Free Cities rely on mercenaries for the same reason that the city-states of Renaissance Italy did. Standing armies are seriously damn expensive: while it’s something of a chicken and egg scenario, it took the emergence of the nation-state with its formidable bureaucracy to pay for the armies of the early modern period, and even then there were a lot of bankruptcies in the process before they got it right.  

If you’re a businesslike commercial republic, it doesn’t make any sense to absorb the immense costs of a standing army and the concomitant waste during periods of peace, when you can just rent a mercenary army for however long the war lasts. (And you thought the gig economy was new!)