Sorry to bump this thread, but I saw that it never really did address the "how does this work" question. So I'd like to sort of put a bow on this thread by addressing that exact question.
It's helpful to think of these sockets as torque sticks in reverse. Torque sticks reduce peak torque by diverting some blow energy into twisting the stick. When the blow is over, the stick untwists and wastes the energy it stored while acting as a torsional spring. The less torsional stiffness the stick has, the more energy it stores and wastes and the lower the torque it transmits.
While a torque stick is an extreme example of having super low stiffness on purpose, there is no drive system that is perfectly stiff. So you are always losing torque due to the lack of stiffness between the impact gun and the bolt.
But what if you could take up the slack in the twisting stiffness? What if you could pre-twist the extension such that when you applied an impact with the impact wrench, the extension couldn't store any more energy? Now instead of wasting energy on the lack of stiffness in your system, you would all but eliminate the transmission losses.
This is how all these heavy sockets work-- whether a flywheel design like the IR, the brute force approach of the Lisle thickwall sockets, or the more engineered approach Astro is taking with their hollow drum design. They all accomplish the same goal.
That is this: they add enough moment of interia to the drive system that it cannot "unwind" before the next hammer blow is applied. Thus, they do not waste the energy that was initially spent twisting up the drive. And therefore each impact blow can build on the prior impact blow without having to re-deflect the entire driveline again. This drastically increases overall efficiency and enables you to remove bolts you might otherwise not be able to.
The Astro and IR designs are IMO best because they increase the MOI primarily by a larger radius-- not just through a slightly larger radius with a huge mass increase (like the Lisle sockets).
You guys who said "resonance" were on the right track-- it's a torsional resonant frequency thing. The lower the BPM of the impact, the harder it is to get the next blow in before the system wants to unwind and waste that energy.
Incidentally this is why most torque sticks are useless on cordless impacts. Cordless impacts usually have much higher BPM and lower peak force, and they easily defeat the torque stick.
Just as torque sticks need to be below a certain maximum BPM to work, heavy sockets need a certain "minimum bpm" to work because their own resonant frequency, if higher than the BPM, will cause them to unwind before the next blow is struck.
One of the best insights a respected engineer ever gave me is "everything is a noodle, it's just that some noodles are stiffer than others." Everything deflects from every force. It's always and only just a question of scale.