How does adding latent heat reduce the sensible heat? Are the clothes washed in very cold water?
It relies on the air not being saturated (and for real effectiveness, requires relatively low humidity). It's quite popular in dry climates in the form of a "swamp cooler".
You're not adding latent heat to a room, you're adding water, which when evaporating uses up the heat energy in the room which cools it down.
Look into how swamp chillers work.