Balancing reasons; if the Falcon had a front-firing gun, as well as two door gunners with MGs or GLs, then the helicopter would be like a flying tank. This is the same across all multiplayer game modes, except co-op campaign.
The chaingun by itself would make it overpowered. The GLs are also overpowered as they can fire pretty rapidly and would probably kill i two hits. So machine guns are the best way to go!
the same reason that the falcons "suicide seats" arent useable outside of campaign, it would be a flying killtacular with more firepower then any other vehicle, and the pilot has the best view camera-wise in the falcon, anything he/she sees(which is pretty much everything) would be a target