I feel like if you just make rank associated with numbers of players willing to trust you then it would be the easiest and most fair solution. I don't think you need a direct vote but rather voting by association.
The role selection screen could really use a general revamp. Players are essentially choosing a unit and then 9/10 players are picking private, so the screen shouldn't emphasize the roles like traditional games use weapon classes. The officer and NCO roles would automatically mean you have the trust of other players and people might be more likely to follow them. The organization is important enough that it shouldn't take a back seat to a map or an objective progress bar or anything else.
For limited regiments (Cavalry, Sharpshooters) you need to take into account that some people would initially volunteer to lead in order to try and secure a place in that regiment. You can deter this by not allowing people to spawn in until they have followers.
Also a start-of-round planning phase would greatly help as well.
https://youtu.be/HN8XZJ4RgPU