Why is LOP (lean of peak) controversial?

"Peter R." wrote:

In my case, my engine's cylinder head temperatures rarely get above 310
degrees F and most times operate in the 285 degree F range during cruise
flight. The times they do climb to 310 or 320 degrees F is when I am
climbing to altitude on a very hot day.

I should have included that 380 degrees F is considered the absolute top
end of the safe temperature curve, at least according to Tornado Alley
Turbo and GAMI, both of whom have done extensive testing of LOP operations.

Even on a hot day at higher density altitude (and effectively less ram air
cooling), 320 degrees F is the highest I have seen my cylinder head
temperatures reach.

--
Peter