I respectively disagree. Sway bar bushing don't do anything but provide location for the sway bar. There may be some incidental forces as the suspension moves, but I believe that the rigidity of the frame makes those force inconsequential. Hence, sway bar location brackets are flimsy.
If this was the case, then the sway bar would simply rotate in the roll direction rather than flex or resist motion.
In order to remain static, the total forces in the X, Y, and Z axes must be zero. But the total moments in the roll, pitch, and yaw axes must also be zero.
If we model the arms as being in the X axis only, the links as being in the Z axis only, and the torsion bar as being in the Y axis only, then we have a roughly simplified model of the assembly.
The links can only provide a force in the z axis, and the bushings can provide significant reaction force in the x and z axes (the torsion bar is inside them) as well as incidental force in the y axis (the arms can rub up against the bushing).
There are no significant effective applied forces in the X and Y axes, so any reaction in the bushings will effectively be negligible. But there is an applied force in the Z direction from a sway bar link, which might be explained by the opposite reaction at the opposite sway bar link.
But we also have to make sure that the total moments are also zero.
Moment in the yaw direction will effectively be zero, as there are no significant forces applied in the X or Y axes.
Moment in the pitch direction has already been discussed, but in summary, the moment applied by a sway bar link on the sway bar arm about the pivot must be canceled by the moment on the opposite arm (resulting in applied force on the opposite link).
But moment in the roll direction must also total to zero. The force vectors in the Z axis are not at the same Y position, and also might not be at the same X position if the arms are of unequal length. And as the only other constraint available, this moment in the roll direction must be applied by the bushings themselves.
If one sway bar link pushes up with 20 lbs and the other down with 20 lbs, and the bar is 36” long (guess), there is an effective moment of 30 ft-lbs about the center of the swaybar in the roll direction. This moment can only be countered by the sway bar bushings, and if we pretend they are also 36” apart (they’re actually slightly closer together than the bars), then they will have to counteract the moment by applying 20 lbs down and up at either end to create the 30ft-lbs moment to cancel the roll moment applied by the sway bar links.
So to be effective, the sway bar bushings (or brackets) have to be able to take as much force as the links can provide. Without the reaction force of the bushings or brackets, the bar doesn’t twist - it merely pops up.
Here’s a different way of thinking about it - a sway bar resists roll in vehicles by applying a restorative twist to the axle. That twist must be reacted upon by something else, which happens to be the frame of the car. The sway bar merely creates an additional moment between the axle and the frame.