There have been two interesting concepts brought up in the last couple of pages.
Equipartition theory is useful to highlight how molecular collisions drive the creation of radiation but it does not describe reality because there is a temperature gradient in the atmosphere.
You will have to explain your thinking more. If there is a gradient, a small local volume of air at any height will be largely at the same temperature, and the equipartition of energy will hold for that volume. Equipartition was brought up only to show the mechanism of how an ensemble of atoms behaves, and that it is not a failure if a molecule absorbing IR is not the same to emit IR.
Another related concept is that solar input is both high energy and highly ordered. It is capable of doing work. Surface IR is much less ordered and lower energy. Atmospheric IR is less energetic still, and almost completely unordered and diffuse. Entropy has increased as solar input has performed work on the Earth and waste heat has been discharged into space.
One of the main problems with the models is that they treat waste heat as the equivalent to solar input. It is not. The potential to create entropy has been used up. The work has already been done.
In thermodynamics, work means mechanical energy, like the movement of a piston. I don't see that sun energy directly causes work.
The sun's energy is not highly ordered since it is BB radiation. It is ordered only in the sense that the rays are almost parallel, but I don't see how that would affect things.
Yes the surface and atmosphere are less energetic insofar as individual photon energy. The important issue is the total energy of the sun directly warming earth, and the larger total energy leaving the surface as BB radiation.
In thermodynamics waste heat only has meaning when there is a transfer of heat to mechanical energy, such as the wasted thermal energy out of your exhaust in a car. Mechanical energy does not have a major involvement in climate physics, except maybe for hail stones, heavy rain, or wind moving something.