>The big generator of entropy is just the thermalization of sunlight
How do you know that?
There are volcanoes under the oceans spewing incredible amounts of hot gases into the floor of the oceans and much entropy generated from that, which in turn MIGHT be warming the atmosphere as well, over 100s of millions of years. Why this entropy is not considered or measure as negligible.
Generally I need to question every statement as such and all the math and computations, my intuition tells me almost all of us are generally mistaken about the atmospherics dynamical systems