Think of the King and JKS doodad as an accessory to a sway bar, be it factory or an Antirock. The small road events that might toss the Jeep side to side via the sway bar will be soaked up by the doodad. Once the doodad reaches the end of its travel, the main sway bar takes over and will behave normally.
While they may allow a stock bar to flex a bit more, these things don't take the place of a softer rate bar like the Antirock.
I don't have a reason yet, but I feel like this is a better job for a spring like JKS, rather than a damper like King. Longevity, perhaps? Springs don't leak.
I would really like to try one of these on an AR, especially with my usual recommendation to run the AR as stiff as possible without limiting the flex allowed by the shocks. I don't see myself changing the little springs, once I found the rate that I like. Cost keeps me away from trying it.