Actually, if everyone perfectly tailgated out of a rolling jam, then they'd all be fine. Instead you get people that let a large enough gap open for them to accelerate faster than the car in front, then they have to brake when they reach that lead car again. This slinky effect is what causes those rolling traffic jams and why they can break them by slow-rolling in from of the jam to force everyone to stop the slinky effect.
I imagine phantom jams will pretty much be a thing of the past once we reach a certain percentage of cars running auto-braking cruise control. Have there been studies on what that percentage is?
You have to characterize the control behavior to model whether the system will dampen its response or create a sustained or amplifying feedback loop as all the agents interact. These traffic jams are essentially standing waves propagating between agents.
You don't erase the standing wave by having everybody maintain a fixed following distance or mimicking the speed of their leader. You need to predict future changes and allow the space to contract to help smooth out the transient disruptions and slowly rebound without over-shooting. You want each following car to react less than the previous and have a weaker deceleration/acceleration curve.
Unfortunately, I have noticed increasingly absurd feedback loops in long distance routes here in CA. As a user of conventional cruise control, I can't help but notice how frequently I now have to intervene to adjust speeds in relatively light traffic conditions. On long drives like LA-SF via I-5, these yo-yo drivers are my new nemesis. I don't know if it is due to their use of adaptive cruise controls or a more basic loss of attention or self-awareness. For example, I see packs of cars with speeds oscillating between 55-80 MPH when conditions should easily allow a steady cruise at 75 MPH.