And this isn’t all entirely theory, we have a good guideline for how the private recruitment of violence specialists might work in a pre-modern or early modern context because of course there were quite a lot of mercenaries getting recruited in pre-modern or early modern contexts! And what is striking is that even in cultures where the aim was to recruit farm boys (because they were assumed to make better soldiers than city-dwellers; this was the dominant assumption in early modern Europe, for instance), you recruit them in a town. Or in many cases, you recruit them outside of a town. A lot of towns, quite understandably, are touchy about letting armed bands of violence-doers inside the city walls and if they have the political and security position necessary to forbid such groups entry, they usually will.
So for a society which has need for a second kind of ‘violence specialist’ (beyond regular soldiers or knights or what have you), who specialized in what we might term ‘monster removal,’ you might expect the local political authority (who would be the largest employer of such), to set up a standard place for recruiting them, perhaps just outside the town/castle/city walls. It’s not hard to imagine a combined inn/tavern springing up next to that, to cater to the traffic, and thus get roughly to the ‘fantasy tavern.’ That said, I find myself wondering: if a locality has so many ‘monster’ related problems, why is the king/lord/state contracting adventurers on a one-off basis? Why doesn’t he have them on permanent retainer?
The easy answer, from a world-building perspective, is to make ‘monster’-type problems rare enough that there isn’t any cause to keep adventurers on permanent employment, but that is the death of the fantasy tavern, since it would lack the kind of continuous clientele necessary (instead, we might imagine adventurers functioning something more like itinerant craftsmen and other specialists in such a world).
The other option I can think of would be some kind of guild, with a legal monopoly on offering ‘monster removal’ services. Often ‘adventurer’s guilds’ in fantasy worlds are vast, continent sprawling institutions, but we ought to expect this to work like other guilds: extremely local, perhaps with each large town having its own guild of adventurers which controlled membership, extracted fees, regulated the trade and provided for widows and such – the sort of things historical guilds did. In that case, the place you would go to hire an adventurer wouldn’t be a tavern, but a guild hall. It might well have some of the same facilities (a kitchen, dining spaces, lodging), but they would be for the members, rather than public. Such a guild would then have a fair bit of price-setting and bargaining power, even potentially against the state or local lord. Of course, they’d also have a role in preventing non-members from offering services – one might expect rather violently.