The ring will change the resonance frequency of the DS, and was likely to alter/avoid a resonance in the driveline in a particular vehicle under particular operating conditions. Those conditions would likely be potential for resonance, and not every identical car would experience it.
Heavier items tend to 'absorb' vibration, too. FWIW, many C-bodies have that inertia ring.
Back in the early 2000s, there was a vehicle combination with Navistar trucks: DT466, Allison 1000/2000-series AT, and long WB with single drive axle.
A common configuration for rental-fleet box trucks.
Due to some natural resonance of the DT466 engine bellhousing, Allison did not permit the DT466 to have 6th gear, which might've excited that resonance.
So they were programmed as a 5-speed only.
There were some of these vehicles that had transmission failures, sometimes repeat failures after rebuild and or replacement.
2 problems were eventually found: some trucks had an out-of-spec driveline, and/or some had engine misfires due to faulty injectors (or both!).
Both conditions were too mild for the driver to notice and report for repair (esp in a rental truck).
End result - the misfire and/or driveshaft vibrations caused enough torsional activity to damage a planetary carrier in the transmission, to shear off a splined snout that engaged the upstream sun gear. That carrier's snout was loaded in 5th gear.
Not all box trucks of that configuration experienced the problem, but enough to capture Allison's attention that something was amiss (pun intended).
So - swapping an old car to a different driveshaft without the inertia ring might not show a problem.
