The reason for changing oil when the engine is hot is to avoid the settling of dirt and water in a cold engine. When the engine is fully warmed, then drained, a higher percentage of contaminants are drained away with the old oil. When the engine is drained cold, more of these contaminants remain in the oil in the bottom of the pan, which results in more contaminants mixing with the new oil. If you don't change the filter each time, the new oil will automatically start off with one quart of contaminated used oil. And new filters are simply more effective at trapping contaminants.
Old filters can serve as an excellent indicator of engine condition.
An old filter that's been removed and cut open can provide an indication of the engine's condition by the amount and size of the particles in the filter. If your engine isn't equipped with an oil filter, the pressure screen should be monitored. The pilot or mechanic should always review the manual for proper procedures. For example, on most engines an inspection of the oil pan's suction screen is recommended at each oil change. Many of these checks seem to be a waste of time because one rarely finds anything.