If carbon dioxide (CO2) simply absorbed energy, including sunlight, without re-emitting it, it could lead to cooling at the Earth’s surface. This is because the absorbed energy would not be radiated back to the surface, resulting in a net loss of energy from the Earth-atmosphere system.

Hmm, I don't follow the argument. If the CO2 and other atmospheric molecules were unable to re-emit the light, they would need to dissipate the excess energy via non-radiative processes. So the main transfer of energy to the surroundings would be via collisions with other molecules. The density of molecules is greater as you approach the surface, and the density in space is very very low. So there are many more molecules to collide with that move the energy in the direction of the surface, and there is no easy pathway to get the heat out of the earth, other than hot molecules diffusing into space.

So, unless there is an important hole in my reasoning, removing the radiative pathway would ultimately result in a hotter earth because a larger percentage of the energy of light is trapped.

I think that the main problem in your comment is that it does not account for what happens to the energy that is absorbed. This energy does not disappear - you need to account for it.