Hey. I'm a helicopter mechanic, and may be able to shed some light on this. You're confusing the balance bar (CX, CX2) with a flybar (CP, CPP). They perfrom 2 different tasks.

Helicopters have a natural tendency to rotate opposite the direction the main rotor is turning. Most helicopters use a tail rotor to counteract this torque. In the case of a coaxial heli like the CX & CX2, it uses an additional main rotor turning in the opposite direction to cancel the torque. Even though you have two main rotors, you still need one to perform the actions of a tail rotor and one to perform the actions of a main rotor, or the aircraft would be completely uncontrollable. That is why only the lower blades are linked to the swashplate. They change pitch to move the aircraft in flight. The balance bar keeps the upper blades level relative to the orientation of the aircraft. This provides a constant source of lift and stability regardless of what inputs may be affecting the lower blades. The CX/CX2 then uses variable motor speeds to facilitate what we call pedal turns (we call them that because the foot pedal controls in a helicopter control the tail rotor and cause the aircraft to pivot around the main rotor shaft).

The purpose of a flybar is a little of the same concept, and a little different. First there's some facts you have to take into consideration. I'll use the UH-60 Blackhawk helicopter as an example. The blackhawk in flight configuration weighs about 14,000 lbs. The main rotor turns at about 250 RPM and has 4 blades. In comparison, The Blade CP weighs about 2 lbs with the main rotor turning about 2000-3000 RPM with 2 blades. The sheer inertia alone in trying to move a 14000 lb aircraft creates some stability in addition to force dampers and other systems. Hence the flybar on the CP. The flybar is heavier and will maintain a more stable rotational plane during in flight forces than the lightweight blades would. That is why the swashplate is linked to the Flybar , and the flybar linked to the blades. The flybar basically forces the blades to align themselves in the same plane as the flybar. A direct linkage at this weight at that rotational speed would make the aircraft too responsive to control. The Bell-Hiller head for the CP/CP Pro has a direct swashplate to blade linkage in addition to the above configuration, and even though it still has the flybar, you can really see the difference in responsiveness. A buddy of mine flew like a champ with the CP. When he upgraded to the CPP, he crashed and almost destroyed it 1st time out. It's extremely quick.

Anyway, hope I helped a bit.