Well, I'm not Brendan and I'm not an oil expert, but I will tell you what I have been told.
Several years ago I was a manager of an auto parts store. One of the wholesale warehouses had an open house where manufacturers had booths showing off their products. Here's what I learned from an oil company's sales rep.
An engine with an oil filter should use detergent oil. Detergent oil dissolves dirt in the engine and absorbs it. As the oil circulates through the engine it passes through the oil filter and the dirt is removed and clean oil continues on it's way.
An engine without a filter should use non- detergent oil. The dirt is not absorbed by the oil. It circulates with the oil into the pan where gravity cause the dirt to fall to the bottom of the pan. The oil pump pick-up is slightly above the bottom of the pan so clean oil goes back through the engine. When the oil is drained the dirt in the bottom of the pan is washed out with the oil. If oil is not changed often enough the dirt level in the pan will get higher than the pick-up and cause dirt to circulate through the engine over and over.
If you use detergent oil in an engine without a filter the oil absorbs the dirt. The dirt does not drop to the bottom of the pan. It just recirculates through the engine over and over.
Now, as I said I am not an oil expert, but this explanation was told to me by an "oil expert". The logic made sense to me. If this info is not correct I hope someone will let me know.
