Would you care to elaborate on that? I did already, you just failed to copy and paste the rest of the answer.
Formation of CO2 releases more than 3x the energy of CO. OK, and by running richer and richer you generate a lot more CO.
The rest of the answer didn't say anything about the amount of energy released.
When rich by definition you are limited by the amount of O2. If you produce CO instead of CO2, you can only get 2 x CO for every CO2. Not "lots" - exactly 2.
2 x 1/3 = 2/3, which is less than 1. For each 2 CO you produce, you lose about 1/3 the energy you would get if it was less rich and the O2 ended up as CO2.
My high school chemistry calculations (admittedly with 25+ years of rust)
Don't worry….I am worse off 
suggest that 10% excess fuel reduces the energy (heat) released by about 3%.
Not really, it slows down the burn rate, and the peak pressure occurs later, therefore at a lower peak pressure.
Yes, really. The energy (heat) released is well documented. More CO = less heat.
The chemistry says less energy is released.
By definition, EGT is lower when richer than peak EGT.
Full rich generally gives lower CHT.
So I don't understand the claim that fuel doesn't cool. If richer mixture doesn't cool, where does the heat go with all these cooler temperatures?
Maybe "fuel doesn't cool, it just heats less"? Of course it may not be the most efficient way of cooling, but it doesn't mean the effect doesn't exist.