Heat picked up at the surface is
thus rapidly vertically mixed and transported by all three mechanisms — conduction, convection and radiation — acting at different length scales and with considerable and non-ignorable
chaotic and self - organized emergent mesoscale structure — to produce an atmosphere that, as you note, ends up somewhere between the DALR and isothermal most of the time, although inversions (warmer on top) or with a gradient even larger than the DALR happen all the time, and are unstable or transiently metastable
states with some lifetime and break apart and perhaps reform somewhere else as the conditions that favor them recur.