I have a long running campaign where one of the characters is of much higher social standing than the others (he is a landed noble now, and before was noble with no large holdings) as well as independent income from his family holdings. I agree that in the middle ages social standing mattered a lot, just as it did in Imperial Rome. However, human nature and reality also lead to people being friends and to a degree ignoring these differences when removed from societal surroundings (adventuring for example). The noble is more or less the "leader" and he tends to let his people do what they do, the others do not show flagrant disrespect for him around others, especially nobles, and they largely benefit from "working" for him (gear, supplies, etc). I think the players matter for this sort of arrangement though, and I could not see a scenario where strangers who played together could make that work without a few ground rules.
The arrangement has led to some very interesting situations and role playing as well. Cimmerian Barbarians are often a bit willful and strike out on their own when the mood hits and the noble is entertaining gentry at banquets.
I am considering a campaign where the characters are part of a rogue trader crew (WH40K setting), but in that scenario, I do not know that I would be as comfortable allowing one of the players to actually be the captain, maybe a cousin or son of the captain who "must prove himself", but a rogue trader captain in many cases has as much or more power than a literal king of a powerful nation, and I do not know that my players would be ready for that sort of game right out of the box. I might have some very loose chain of command, but more similar to a junior officer learning his business from senior enlisted types, rather than a captain and crew.