A diversity of views. I was wanting to get a cross section of opinions, and try to see where the confusion exists.
Based on a deep look, evaporative cooling does increase oxygen densiity. At 1 atm and 40% humidity, it does so an average of 7%
At 3 atm and 500 F (COT), it will do so an average of 15-20%, though it is hard to find data at high temp/pressure. Nothing to sneeze at. I'll explain.
If you are in Mississippi, 90% humidity, when that air is heated in the compresor to 500 F, it goes to 3% humidity. That same lb of air can hold 30 times more water, well kinda/sorta. As water is evaporated in that 3% hot air, temp comes down quickly, and that RH goes up fast. RH is very highly dependent on temp.
Anyone really wanting to understand how that works, get a text with a psychrometric chart, and work a simple evap cooling problem. It describes the relationship between moisture and air.
This may clear up some details. True, 90 degree 100% RH air has less O2 than 90 degree dry air. But that is irrelevant. We will take that 90 degree dry air, fully sturate it to 100%, which brings THAT air temp down to 40 degrees (guess). The air experiences an increase in density from the temp change, AND a smaller decrease in density from the space occupied by the added water vapor molecules. Hope that is clear. The overall impact is increased O2 density, and increased N2 density for that matter.
Methanol is a separate discussion, since it has fuel considerations.
good discussion.