Could sprinkling cool water on the runway in hot summer decrease air density? Why is there no such technique used where cool water gets sprinkled on a runway?

Cooling down the air above the airport would decrease air density and therefore lead to a shorter starttime for airplanes.

This image explains exactly what I mean. 

(related article: https://www.boldmethod.com/learn-to-fly/performance/prevent-a-density-altitude-crash-on-takeoff/)
There are a few problems with this idea:


The water evaporating would increase the humidity, likely canceling any cooling benefit.
The effect would be localized in a very small region just above the pavement.
The effect would be temporary as any breeze would quickly blow the cooled air away.