From what I have read so far there are two origins for this.
Back in the 1920's there is a lot of 'talk' that rapidly cooling an engine (running full speed then shutting the motor off) will warp just about everything. Evidently back in the day cool downs were uber important. But also in the 1900-1920's people were tinkering with motors and the ICE was very new.... so most of what is documented can be attributed to either poor material quality and poor design. I know of no aircraft motor that required a cool down, most had no exhaust other than a short tube (if that.. rotary engines were common in AC) and most, if not all were shut down immediately after landing.
This is a Sopwith Camel Clerget motor.. open exhaust Over 5000 Camels were made, so if there was an issue with open exhaust valve warping someone would have said something.
Second, taking off headers will reduce back pressure and lean out your mixture. Very lean mixture can lead to burned valves and very high cylinder temps. I'm gonna say THIS is the main reason why (since the 40's) that people think they need headers. Take a motor with a carb mix set for X back pressure it will run fine. Remove the header and now the motor moves MUCH more air, and the carb is not jetted for to account for the increase, leans out the mixture and burns the exhaust valve/warps it due to high temps. But since the 'only thing done' was removing the manifold TA DA! A new myth is born!
