The issue is they don't get rid of humidity, they actually create more. On super hot days when it's like +30 it would probably even start to cause water issues as the pipes and toilet and other items that have water in them and are cooler are already condensating quite a lot as is. That's probably why they say not to run plumbing directly above the electrical panel. When it gets really hot the pipes condense and can drip. My main passes dangerously close to it and it always makes me a bit nervous seeing all those water droplets. Not an issue anymore now that I have A/C though.
Also depending on the source of the water, they may not even cool the room/house down at all. Ex: if you are just using tap water that water is already in the house in the pipes. Suppose if you let it run long enough until it's very cold then you are getting water that is colder that does not originate from the house. You can think of the house as a closed system, and if you consider the laws of thermodynamics you can't cool it without interacting with the outside.
Same with those ice bucket AC units people make where you put ice in a bucket and have a fan blow over it and there are holes. Those are only effective if the ice was made outside the house. If you're grabbing ice from the freezer and then making more, the energy required to make that ice is going to generate more heat than what the ice will cool down.
Traditional A/C units work because of the outside unit. The heat is "sucked" into the coil of the indoor unit which is why the coil gets really cold, and then the heated gas travels outside and then the heat is expelled through the outside coil. There's a whole science as to why that happens and basically has to do with the compressing and expanding of gases. Kind of the same idea as why rubbing alcohol makes your hands cold. They suck the heat out and then it evaporates.
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