It depends how historical you want it to be, it was uncommon for there to be training facilities in every region during the time period, this is when the world was moving towards standing armies and a more centralised system, compared to the vassal/levies of old. Recruitment posts and trained soldiers are two very different things, so I still think distance from capitol should be a major factor in resupply rate, how that is worked in I've given my opinion, but I'm sure others can give it more thought.
But keep in mind how atrocious the AI can be in the game as it is, if reinforcement/supply was made significantly more complicated, I'm pretty sure the AI would fall over horribly with it. They find forts and zones of control hard enough as it is.