Death Wobble

Any solid axel suspension system has a natural oscillation tendency due to the length and flexibility of the suspension components and the flexibility of the tires. The stabilizer is there to soak up the oscillations. If it is too pliant then it won't soak them up, and if it is too stiff then it will conduct/promote oscillations as if it was a rigid member. If the stabilizer is not selected based on complex computations, it may be selected based on testing or experience.

This is why using the OEM stabilizer (or one proven by many based on actual experience) is a good idea. It is said that Jeep's current stabilizer has improvements over the the one that came the first couple of years of JL models. The improvements lessen the chance of "death wobble".
The purpose of the steering damper (or stabilizer) is to damp out shocks from the road that can affect steering system all the way up to the steering wheel. In the days before power steering, the steering damper was used to reduce the chance of the steering wheel being ripped out of the driver's hand when the tires hit imperfections in the road. With the advent of power steering, the problem was reduced further and with modern power steering, virtually eliminated.

If there are noticeable oscillations in the steering components, there's a problem. A steering damper can help but it's a bandaid (Looking at you, JL, JT).
 
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