Why is cooling by radiation more important at higher altitudes? I can see how the inverse would be true: that heating by absorption would be more important as a mechanism of heat transfer at higher altitudes, simply because there is no surface to conduct heat to the air at high altitudes. I guess what we really need to know is the net effect, in terms of relative importance, as to the effect of greenhouse gases to heat transfer as a function of altitude. If it turns out that air at high altitude emits radiation at a higher rate than it absorbs then this is unstable and convection may ensue.
Of course, we have convection, and we can explain it without the need to resort to this effect. Then we may reasonably ask, how important is this effect? What is the relative order of magnitude of this effect in relation to the standard model of atmospheric convection: hot air rises, expands and cools, advects, and sinks. Afterall, the concept of the Hadley cell, which fits global observations of convection patterns neatly, does not rely on this effect. This might suggest that this effect, if it exists at all, is negligible.