belt driven means it is running the whole time the engine is on, pumps wear out even if not under load, but it's gonna be a functions of the pump quality and the cleanliness of the oil circulating in the system
i think when a pump is direct connected to an engine it's referred to as a "live pump"
old timey tractors had options for live pumps and ones that were engaged via gears and the clutch for this reason
the live pumps were not ordered as regular equipment unless there was a good reason for it
my 1950 farmall tractor had a live pump, it is so worn out it could not operate anything,
it has the same big round filter as in that first photo
-s
