The primary idea behind an Aux oiler is to reduce B&C wear and to a lesser extent take some load off the powerhead. I have a temp gauge on my powerhead and found that water lube did not reduce the powerhead temp any more and maybe less than oil. The only benefit I found was that I could touch the B&C sooner and yes it does keep the chain cleaner but so does using enough aux oil.
I have milled some 30 Aussie hardwood logs (most would be harder when green than Hickory is dry, as well as being very gummy) using water cooling in place of Aux oil and found the B&C wear was a clear problem. I also tried hooking up a running hose to the aux oiler point so I could use larger amounts of water and it made no difference - if anything it was worse.
The analogy with the tool steel cutting is not valid as tool steel does not constantly slam up and down against a workpiece like a chain does on a bar. Most people don't realize that only about every 3rd cutter on a chain takes a significant bite into the wood and this lifts a short segment of chain up off the bar. The biting cutter rocks it's way further into the wood until the tension on the chain builds up so much the leading cutter tears out the chip and the chain slams back down onto the bar. Water cannot sustain these sorts of pressures and is quickly squeezed out between the B&C dragging any regular bar oil with it.
All good points sir although my experience with 2 strokes and the type of "metering" carburetors they use shows that a cylinder or head temp gauge can be essentially useless. But that's another thread for another day, based on my experience with air cooled engines operating on the restricted throat principal. So assessing the load the engine is seeing based on temperature is very unreliable.
Now I totally and whole heatedly agree with your points above about water, so I want to clarify that I am not talking about plain old' water. But rather water that has special additives dissolved in it, that give it lubricating properties far superior of any oil. While cooling at the same time.
Here is my thought process, milling puts excessive amounts of long term friction into a bar and chain which results in heat build up, causing the chain to stretch as it expands and the bar to swell closing the gap the chain rides in. This all causes the designed tolerances for each part to change, changing and reducing the ability of the parts to hold oil and be lubricated properly and the oil to break down reducing its effectiveness. If you keep the moving parts cool they will operate as designed, which is what the water does. But that in turn removes the oil which lubricates. Water caries heat away better than oil. Water is plentiful. Water does not lubricate. But, there are additives available which allow it to do so and are safe to use.
My idea is to do away with oil completely, as with the machining analogy, and only use a lubricating water based coolant. The stuff in have in mind cost about $45 a gallon. One gallon mixes to 50 gallons with water. I this biodegradable, environmentally friendly. And ever year our supplier rep replaces the oil in a 16 HP generator and runs it at full load with the water coolant mix for an hour just to show its abilities to us. Something we all look forward to every spring.