A little clarification if I may?
The majority of cars have constant mesh transmissions.
Synchromesh and dog are not mutually exclusive; or to put it another way all gear engagement is achieved by a 'dog' or one device sliding in or over another. It is simply that a synchro is a braking device.
Some cars DO have synchro on reverse by the way.
To quote from the advised website "However, it happens that the noisy rattling in neutral is also an issue in modern, emissions-optimized automobiles. The manufacturers have resolved the problem with a so-called double-mass flywheel, which dampens the torsional fluctuations before they can reach the transmission input shaft."
The reason for DMF is NOT to subdue idle chatter, but the far more troublesome and damaging effects of loaded gear chatter. Most powerful manual transmission cars for instance will set a resonance with the gear, clutch, flywheel and crankshaft when high load and low engine speed are demanded. 15 mph in 5th gear for instance. The DMF is tuned to cancel the resonances and act as a cushion. The drawbacks are as mentioned increased mass and complexity. Anyone owning a 911 Porsche, from whatever vintage, will understand this immediately!
Idle chatter (if relevant) is generally contained by the specified idle speed.