There are many more experienced pilots than myself around here who would be better qualified to answer this question, but I'll do my best.

In the case of the CX/CX2, the flybar acts as a means to stabilize the heli. The weights on the flybar create a gyroscopic effect that serves to keep the flybar in place while the heli moves around. The link from the flybar to the upper blades causes them to pitch in the opposite direction from which the heli is tilting, resulting in self-leveling and a very stable hover. The trade off, of course, is mushy flight characteristics.

So, the more you reduce the gyroscopic effect of the flybar, the more responsive and less stable the heli gets. At a certain point, the heli becomes impossible to fly... by a human at least. Your example of removing the flybar and locking the upper blades would likely result in some very short "flights".

Shortening the flybar and/or removing the weights is a good overall compromise between stability and responsiveness. It makes for a heli that is not well suited to beginners, but good for someone looking to try something other than hovering.