Possibly because they are designed and engineered and tested to be able to run at those settings for the TBO of the engine?
Yet so many of them don't make it to TBO.
Again, the data shows what one problem is, because there is a real life experiment going on in aviation land. A fairly homogenous group of pilots - fed about the same diet of folklore and facts during training - some flying brand X engines and some flying brand Y engines, and brand Y is suffering far more premature cylinder failures/valve problems. But what's the explanation? It couldn't possibly be the manufacture or maintenance of the cylinders and valves on brand Y engines. Gotta be a pilot problem! Get aircraft owners to pay for a fleet wide change! Further, a bunch of pilots flying brand Y LOP gets fewer pre-TBO failures that pilots flying brand Y ROP. LOP must be bad!
It all makes perfect sense.
There are also some assumptions about what is hard on the engine - specifically heat and high cylinder pressures.
"Assumptions" is an odd way to describe the realities of the metalurgy involved in what is, after all, nearly century old technology. Why did the designers put a red line on CHT?
I'm confident that there is data to show how strong the materials comprising cylinders are at various heats, and what happens when various pressures are applied to them.
Other things that could be hard on the engine:
Could be. Might not be. What do the data show?
Certainly the data show that running the engine longer and more often is better than running it 1 hour every couple of months. Not sure what that has to do with ROP v LOP though.
[Y]ou are least likely to have problems if you operate in the way the designer expected ... [s]ince he is the one that knows the design intent.
So are you saying that the designers of piston aero engines never expected them to be operated LOP?
If so, it's astonishing that those designers were blissfully ignorant of the tens of thousands of piston aero engines that have been operated LOP for millions of hours over many decades as standard operating procedure.