Well - what I have done by lowering the air temp is raising the amount of oxygine awaileble to the engine.
When you have more oxygen in the mix, you generate more Kw with the same amount of Fuel.....
If what you say is true - your engine would work just as good in high altitudes in thin air - is dosen't. It's depraved / starved of oxygen. This is well known
When you add NOX you increase engine work / power-output / Kw at a given RPM.
When the tractor pulling guys inject waterdrops they increase oxygen levels.
When you turbocharge an engine you put more air thus also oxygen in.
Oxygen is the critical factor in the petrol / gas mix to produce power. Its the "short" factor. The more oxygen you can get in the better for the cumbostion and Kw output. (up till a certain point)
As cold air contain more oxygen than warm air, your engine will produce more power at a given RPM on cold air than it will on warm air.
Thats why you put intercoolers on engines. It's to lower the intake air temp and raise oxygen levels.
Ever tried ridig your bike through a mist or fog on a summer evenig? Yes you can let go a bit on the throttle, as the moisture in the air supplies the engine with more oxygen rich air.
Now - that said - the past 10 year development in engine management progamming has taken a turn wich prioritises emmisions.
So on some engine management systems (EMS) the ECU will "overide" the powergains from the extra oxygen, as to maintain a certain working temp in the catalytic converter, and a certain combustion temperature.
This will to some extent work in the opposite direction of the advantaged of the extra oxygen in the cold air.
But I agree with you - we will never agree on this. We saw plenty of evidence when I worked with this 10 years ago. Sadly I don't have assecs to the data anymore.
So it's down to what practical tests folks can come up with.
But I belive, that it also comes down to how the EMS is set up. If the engine and EMS prioritses lean burn and thus hot air, a HAI will benefit the engine.
So - let agree on, that we disagree