Trackbar, Panhard bar, same thing. Yes, you would think it would lock the axle as one pushes one way and one pushes the other way. I can assure you that it does not coause a problem the truck has enough weight that it is not a factor. I am not sure if it flexes a bit when it drops down or what. The new track bar I built was out out 3/8, and 5/8 plate and the tube is 2" 1/4" wall so its extremely heavy duty As long as you put the bar at the same angle when the airbags are deflated as when they are inflated, it will push the axle but will bring it back to neutral.
It is hardly best practice to have a double panhard bar (one each way). Doing so introduces interference motion.
When the suspension cycles up and down, one or more of the following is happening: the frame rails themselves are being flexed outwards and inwards, the panhard bars are flexing, the panhard bar mounts are flexing, or, if they are resilient enough, the panhard bar bushings are alternately compressed one way and the other.
Regardless, none of those components are designed to handle those sorts of loads, and eventually something will fatigue and break. If a panhard bar or mount breaks, that is a definite inconvenience depending on circumstances. If you frame cracks open, well, that would really be unfortunate. With bars as beefy as you describe, you might well be flexing the frame out and in. In terms of strength from most to least, the pecking order should be frame, panhard mounts, panhard bar (not bars, just 1) and then the panhard bar bushings.
In the mean time, the suspension is stiffer than it should be due to the interference motion, which one might misinterpret as a 'nice firm ride'. Until something goes t1ts up.
With one panhard bar, as the suspension moves up and down the axle wiggles a bit side to side. The control arm bushings accommodate this movement as the axle actually moves slightly out of the centerline of the vehicle..
With double panhard bars, the axle cannot wiggle - if one bar tries to pull the axle to the left, the other one resists, keeping the axle centered. But, just as you say, the axle is going up and down and it is a heavy vehicle. Therefore, and there is no maybe about it, one or more components are deflecting (being bent back and forth). This might be slight, but repeated thousands of times as you drive the truck, eventually the metal will fatigue and crack.
Strongly suggest you remove one of them.