Earlier quoted context omitted.
Swamp coolers cool based on evaporative cooling: water evaporating into dry air reduces the (dry bulb) temperature of the air. So with high wet bulb temperatures indicating air is already saturated with moisture, the swamp cooler won't work.
Dehumidifiers are a thing. I presume that having water and electricity is a bigger problem for most people, but I’d love to be educated more on the problem, if you have links or literature.
Most modern ACs in fact dehumidify and cool in one step with a compressor and then use the collected water to help carry heat away from the compressor by letting the water evaporate into the exhaust to save power (it's why you rarely have to empty water from modern dehumidifying ACs).