I do not understand this shoe thing really.
If you run barefoot (on a surface that is not hurting your feet), you will have minimum LOSS of energy in that energy of movement (up and down and breaking forces) will be stored into the legs muscles and tendons. Depending on your running form there will be a large return of this energy to move up and forward. this is very important for running economy.
If you run on the beach, we all know that we will loose energy in the deformation of the sand both when landing and moveing forward.
Cushioning works to dampen the peak forces because we think that is healty and needed.
There have been done research on what happens with the stiffness of the muscles and tendons when the surface and the shoe cushioning changes. The legs adjust their stiffness according to the softness of what is underneath the feet. So if we run on sand, the legs stiffens, if we run on concrete it loosens up, all to adjust to the a better running economy. So if you add cushioning to the shoes, the legs stiffens and if you remove, they soften up.
Cushioning can dampen and work as a spring. Dampening will just dampen the forces and not return the energy so it is lost. A spring both dampens and returns energy. I guess good cushioning does both good dampening and good energy release, but will always give a loss of energy.
From a point of how the leg works, I do not see why I need such cushioning. Of course I need a shoe that can protect my foot so I can run safely on different surfaces, but since my legs stiffens the softer the "ground" is, I would not win anything by adding something that gives a net energy loss?
A comment is that the carbon plate thing with shoes is another discussion. That does not cushioning, but tries to help the foot moving through the running gait when in contact with the ground. It can reduce the stress over long distances, but if it is better than running barefoot? maybe, maybe not?
Some serious side-effects of cushioned shoes is that it can enable heel striking, which by no means is a natural way of running. If you have to run barefoot, you would never do heel striking... Another side-effect is the excess drop from heel to toe that over time might shorten your calves to the degree you have trouble running in flats or spikes and get sore legs. The new carbon plate help also makes the calves weaker.
So as you understand I am no fan of shoes that f**k up our natural running and I run in minimal shoes even on tarmac. If I do that (I have enough to protect the soles of my feet) I never get sore in the calves. I have a pair of stiffer flats I like so it is comfy with stiffer soles, but not necessary IMO