Simplified: at peak EGT you have stoichiometric mixture, meaning: every fuel molecule has the potential to find one matching oxygen molecule and get burned perfectly.
In a 'rich' mixture, there are more fuel molecules than oxygen molecules, in a 'lean' mixture there are more oxygen molecules than fuel molecules.
The reason both a richer and leaner mixture produce less heat is because they burn less quick and therefore act like a retarded ignition: the peak power pulse happens later in the cycle when the cylinder head has moved downwards more and there is less pressure (and heat) in the cylinder.
Same with single magneto operation: the flame-front needs more time to burn the whole air/fuel mixture and this also acts like a retarded ignition thus EGT rises.
Hottest CHT happens about 40°F before the hottest EGT, so peak EGT is better for the engine than 'enriching slightly for the grandma and kids'
About the savings: in my aircraft, at TBO time, the LOP savings in fuel consumption more than pay for the engine overhaul. The EDM700 has more than paid for itself in reduced engine and ignition system troubleshooting time.
One more reason: at peak or LOP, there is NO carbonmonoxide produced (deadly in case of exhaust/heater leaks)