The mfg knows the tires will gain air pressure while being driven - all tires do it. They want to make sure you don't exceed a certain pressure when cold before starting your trip.
Excessive loads can also damage tires, part of it by generating excess heat. This is why they label the tires with the maximum load.
If they were worried about how much the tire will gain during operation, they would also put a maximum HOT air pressure rating on there.
As long as you follow the max cold air pressure and the max load capacity, the warm or hot tire pressure is taken care of.
Bill