I would run it as all ships are drawn from the same BP pool, and treat them as equal tier. That way, if a player wants to be a fighter pilot, he/she doesn't get blasted out of the sky due to being so low tier compared to the opponents.
When everyone is on one ship (wither space or water based) there kinda needs to be just one person in charge. If the pilot did what he wanted, that could throw the gunners way off track. If the engineer did what he wanted, he could do something 100% useless (Like reinforce weapons, when the crew was just going to be running away anyways).
In any case, having a leader (in this case, a captain) means that everyone is following his lead (or at least should, but that opens up RP possibilities if they disobey orders). The captain may not always have the best plan, but an OK plan executed at it's max potential is far better than a lot of different great plans executed at the same time resulting in chaos, and none of them working like they should have.
In combat, there is no time for a vote. Someone must take command.
Also, from a non-combat perspective:
Going together in a single ship is way different than traveling on land in a typical Pathfinder party setting. On land, if there is a difference of opinion, the party can split, and go its different ways. In a ship, it is all or nothing. The entire party goes one way or the other. There could be a democratic voting method, but the fact is, more often than not, there will be a split vote. Even in an odd numbered party, there will be one half voting one way, one half voting another, and the tiebreaker guy will be sitting there undecided because he doesn't want to go either way. Having a "Captain" is just a practical way of keeping this from happening. After all, you can't just sit in space for a long time if the democratic process can't figure out where the ship should fly.
As for other ideas:
Captain doesn't have to be rank, necessarily. It could be just the guy that has the most common sense (or wisdom :) ) that everyone listens to. It could be the one with the most charisma that everyone likes enough to take orders from. Really for someone to fill that kind of role, they just the respect of the crew, and the willingness to take on the responsibility. No rank required.
After taking a quick look at the starship rules for combat, I've come across a question I hope you guys can answer:
If the crew of a ship can only take one action per round, how is an interceptor or a racer supposed to shoot its guns and move? It seems that RAW the pilot must choose to either fly or shoot, which seems really debilitating for combat purposes.
With the recent end of the war, I also think that can add a lot of good Role Playing opportunities. I'm planning my first character to be a Vesk ex-fighter pilot. Having to join in with races he was fighting against to avoid his old employers. The RP possibilities are ripe for the picking!