Withstanding Peak Temperatures

OK. I have a basic question. Why is running an engine at peak
temperature (as in Rich-of-Peak operation) not good for the engine? In
the scheme of things 50-100 degress cooler than peak temperature (where
many folks recommend the engine be run) does not seem significantly
lower in temperature than the peak temperature. It would seem if the
engine parts can stand Peak-100 degrees, they would be able to stand
peak. What am I missing? (Oh, and I have read Deakin's articles on
AVWEB, and still have this question).

-Sami (N2057M, Piper Turbo Arrow III)