Indeed, that's an oft-forgotten point: We aren't actually part of the regular standing forces of the Grand Companies. Rather, adventurers and free companies are irregular units, and they're nominally enlisted by the Grand Companies to serve as an auxiliary or reserve force.

If I recall correctly, the city-states used to have larger standing armies, comprising not just enlisted/commissioned units, but also large numbers of mercenaries. But after the end of the Autumn War with Ala Mhigo, there was no further need for large standing armies. Many soldiers lost their jobs, and for a while, they were a nuisance until the Adventurers' Guild was set up to provide some form of employment.

I think this was explained in Ver1.0 lore. More experienced lore hounds may wish to correct or corroborate my information.