One faction maybe, but all of them? So, we may potentially run out of Rebel craft while the Empire remains strong, while several other factions could field anywhere from a handful of ships to near as many as the Rebels. This is what the game could potentially look like if we follow that train of thought (all numbers are completely random, to illustrate a point):
Empire: 14 ships
Rebels: 11 ships
Black Sun: 9 ships
Bounty Hunters: 9 ships
Hutt Cartel: 7 ships
Could the game truly remain balanced like this?
Probably not, to be honest. But I for one wouldn't advocate that approach. There's little to no reason to split the crime syndicates and cartels down into individual organisations as the majority of them used similar ships and similar tech. The Hutt Cartels, the Black Sun, the Zann Consortium - all powerful organisations with their own agendas, equipment and infrastructures, but we wouldn't need to see them detailed to that level in game terms, so long as they are clearly distinguishable from the existing Rebel and Imperial forces.
Two Razor fighters and two Cloakshape fighters - a fairly standard pirate wing. Add a Star Viper and you get a Black Sun or Zann Consortium force. Add the IG-2000 and you have a bounty hunter with his hired goons.
As for how they'd play differently to existing factions.. it's a good question, and an interesting one to consider. Pirates, mercenaries and bounty hunters are not necessarily comparable to the elite pilots of the Empire or the Rebellion, and in a lot of cases their tech is not as advanced - so how do you portray that in game terms?
Maybe some kind of advanced "squad leader" tactic - where instead of ships independently assigning their own actions, they are generated by a nearby command ship or squad leader. i.e. the squad leader evades, all unstressed ships within range 2 can also evade. The squad leader declares a target lock, all unstressed ships within range 2 can declare a target lock on the same vessel. Follow the leader, gang up on specific targets, hit and run. Maybe make it stackable, so if you have mooks ships within range two of two command ships, they can generate both actions. The pirate player then has incentive to try and protect his command ships, and the Empire/Rebel players incentive to try and target them first.
This is just off-the-cuff brainstorming of course.