Players have the same personalities, whatever class they play. It's a bigger issue than just which player tends to be more assertive, really, but not really relevant.Usually, one player steps forward the call for votes and brings players back on mission point from tangents outside the GM. That's my experience at any rate. It is often based on the character they play as much as the GM know those are often a refection of each other. However, I have seen the leader shift from player to player depending on characters
I've heard no complaints about the Noble background being conflated with party leadership - either at the table nor around here - but if that's where you're coming from, well, ban the things you need to ban.Enough that its ban by most of the GM I have played with for that very reason.
Unlike the 5e Noble background, though, the explanation of the leader role made it perfectly clear it did not imply, let alone require, party leadership.