Once upon a time, executives at Chrysler got together to find a way to cost the company millions of needless dollars. They decided to put a bar on the back of a Liberty that does "nothing". lol... Of course it does something.
I took my sway bar off a while ago, and instantly my back end would sway back and forth badly while going down the road when cutting the steering wheel left and right. What it was mostly, my upper control arm was shot, and removing the sway bar made the side slop way more evident. The bar is there to counteract side sway (parallelogram-ing of the lower control arms). If the bar was mounted with only one bolt at each end, it would pivot with the control arms and then yes would do nothing. But having 2 mounting bolts locks the two arms together, and the sway bar will fight against side movement. Consider this a quick lesson in physics and geometry.
Back to mine, after replacing the upper control arm, the rear tightened back up, so I left the bar off. I spose if I was in the habit of taking turns like I was driving my Vette, then I might want to keep the bar on.