While I don’t think the player would benefit from having an in-battle presence (just think of how hard it is to keep your original three companions alive and multiply that by a game-over screen), I think that you could get something out of the idea. Basically, the player avatar could have a leveling screen of their own, allowing an experienced company to get some bonuses independent of the mercenaries themselves.
Perhaps you could have skills that make you better at negotiating contract prices, or that make it harder for employers to learn about your double-dealings. Maybe a charismatic captain can attract skilled mercenaries to the company for less gold, or decrease the chance that a mercenary will desert when times get tough.
I’m sure there are other things that the captain could do without being visible, and vulnerable, on the battlefield.
