Suppose you have a problem with the FMC and have lost BRNAV capability.
Many pilots would just tell ATC that they have lost BRNAV without making the PAN call. The reason is NOT that pilots do not know they have to make the PAN call, reality is that they, after advising ATC of the problem, simply forget about it.
Making the PAN call i.s.o. the MAYDAY call is simply telling ATC that there is a problem, a problem that does NOT impose an immediate danger to the aircraft or it’s occupants that requires immediate assistance and priority.
I would advice pilots to make the PAN call in order to avoid the ATC system to overreact and go to code red while not needed.
It’s my understanding from this discussion, which as far as ATC support is concerned while still in the air, the ATC reaction would be the same in case of a PAN or a MAYDAY.
As such pilots have all interest to make the PAN call. If you do not do that then you are putting something on the plate of ATC they want to react to but do not know how.
ATC is a service provided to the pilots but you have to clearly tell them what you want.
And believe me that it can be quit challenging for a Chinese to explain ATC what the nature of the problem is. However PAN, PAN will do just fine.