This system would have to be kept very clean. Dont want standing water or black mold in the walls now, do we?

Interesting idea, obviously best sited to warm dry climates. The challenge might be the water usage. In the American Southwest, for example, water is in short supply. How much would be used by this technology, and would this fit with water conservation concerns?

Would one have to use distilled water? Otherwise would not unsightly deposits accumulate, and eventually clog the bricks?

Luckily there is plenty of water in these arid climates.

where this would work evaporative cooling A/C units are already in use. Unless deionized water is used minerals will build up just like in evaporative humidifiers. Oldguy is right too, mold will be a problem in as you are maintaining a constantly damp surface.

why? would filling the bricks with water be cheaper than cooling the home with AC?

Beat me to it, Oldguy.

3D printing the 16,000 bricks required to build a 3 bed house? Might take a while

Have you heard about the drought? http://droughtmonitor.unl.edu/

This technology would not work in half of Florida as the humidity is nasty here. We cool and remove water vapor from the air in the process. Swamp coolers are inefficient enough to be nonexistent here. The odd ball exception are AC cooling towers for chillers in large buildings like high schools. They use thousands upon thousands of gallons of water and a great deal of electricity to bring water over 90F down to about 80F to cool the chillers which make ice water at about 55 degrees shipped to each area in the building and passed through a coil with a fan to chill the class rooms. Those units are a nightmare to run, maintain and pay for as they are usually poorly designed and often tax payers are on the hook for this junk.