Doesn't that imply you're losing water?

Yes it does. But it might be worth it if you have more water than cooling capacity, or if you have an otherwise very dry house that you'd want a little but more humidified.

Grandparents used to have this. The outer surface of the pot is detectably moist, but not by much, the water level wasnt noticeably lower by the end of the day, I'd say much less than a single cup. Their climate was very dry, crack-your-skin-dry, I don't think it would work as well in a humid environment.

Yes you are losing water but the phase change energy of water is immense, very little needs to be evaporated comparatively for immense cooling.

The cooler water gets, the less vapor it creates.