"The fuel that's not burned helps cool the engine through evaporation." Not very convincing explanation:
The reason a lean or very rich mixture cools the CHT/EGT is that they slow down the flame front. The fuel/air mixture takes longer to burn, placing the power pulse later in the cycle, where the piston is moving more downwards already, expanding more, cooling down more.
Peak EGT and peak CHT are not coincident, they do not occur at the same mixture. The important one is the CHT since it reflects the long term heat dissipation of the head. Peak EGT is already past peak CHT and is a good place to run at 65% or below.