> After berating climate scientists for using mathematical models for using fluid dynamics (driven by huge supercomputers), he turns around and does a back-of-the-envelope calculation like this. It was so disappointing to listen to a brilliant person utterly fail at self-reflection.

This conclusion does not necessarily follow. You can use a very sophisticated computer model based on statistical mechanics that takes into account all particles in the system and their interactions and I can tell you it's wrong using a simple thermodynamic equation. Sometimes a problem is tractable because you get rid of details.