I think I mixed 2 concepts - cooler intake air, and latent heat of vaporization. Both are at work on this rig.

Latent heat is the energy it takes to drive liquid water to vapor. It's why sweating works- it removes energy from the skin as the water evaporates.

I have a friend whose company builds a somewhat similar clever rig for commercial energy conservation. During the night, when electric rates are low, the system chills down a volume of water into ice. Then, during the heat of the day, the ice is used as the means to cool the A/C condensor thus greatly increasing effectiveness of the A/C system - at least as long as the ice lasts and the water stays cool.

There are definite issues with scale buildup and perhaps algae.
I see a little scale on my unit but with 5% humidity on 100F days and not running the water continuously, no algae can grow.