I'm pretty sure they all still have rudder pedals, as well as a separate throttle. Not comparable with a game joystick. The flight stick (yoke) is essentially a combination of pitch and roll.
Just like the right stick on the controller (mode 2). The pedals and throttle are what we have on the left stick.
You CAN/do fly a plane with just pitch and roll. Using the banking angle you can turn while keeping the elevator up. You pull a plane through a turn that way.
This can all be done with one stick, provided you have pitch and roll on the same stick (depending on what mode you use).
A pilot always wants separate rudder pedals. They are much needed for take off and landing in crosswind or bleeding off speed fast, while banking sideways into the wind, as well as steering the nose in the desired direction while in a turn.
With a Phantom however, changing pitch or roll doesn't induce a turn. It will move sidewards (AND DOWN in manual mode). You always need a yaw controller (pedals in a plane) to turn and throttle (of course).
So indeed, if you have a 3rd axis on the stick you could do it.
Separating the throttle from the yaw would be a handy thing for panning shots, because you can concentrate on the panning completely without interfering with the throttle. I find myself often descending or ascending when yawing. I would like a dedicated knob I could twist for panning, overriding the yaw stick, in combination with a non self centring throttle stick. Possible on my next 9-14 channel radio for sure.
Conclusion (mine is) nice idea, however I would prefer to keep things even more separate instead of combining everything in just one stick. It would make filming less ergonomic I guess.