I like the system of hiring and equipping as is (merc camps + tavern mercs), but improvement is not a bad thing either. Historically, Lords contracted to mercenary captains, not individuals, as you mentioned, Nox. So why not make lots of other mercenary captains like the player?
1. There should be other mercenary captains (i.e. landless lords who do not necessarily belong to a faction) wandering around behaving like the player. When you meet them, you can join them or they can join you, or attack them if they are independent or working for the wrong faction, or if you have enough renown you can challenge that captain to single combat to win the loyalty of some or all their troops.
2. Player can found a mercenary camp at any place (like Lumos' outpost kit). Mercenaries turn up wanting to be hired when you have enough renown (a high percentage of routed enemies should turn merc, since in reality deserters or decommissioned soldiers were most often best mercenary candidates). Also when a village gets looted, a certain number of peasants should turn up in nearby merc camps, hostile to the faction that did the looting, to get revenge. You could even have a quest, one of your mercs asks you to nail the lord (or mercenary captain) who killed his family.
3. Also, there should be an option to define your party as a caravan. Trade is the easiest way to make money, for those who don't mind the grind. As a Caravan master, you should get specific quests, especially from mayors, to bring in large shipments of certain goods. Your player icon should turn into a Caravan icon and you get double the storage space. To make this option real, you need high enough trade skill and favor from a mayor, or you can simply purchase or rent wagons that increase your cargo load significantly, but slow you down.