It takes energy to extract water from the air
Why kWh instead of Joules?
The atmosphere is a HUGE energy exchange system. Energy is put into water, turning it into water vapour. That water vapour is transported by the atmosphere. Energy is removed from the water vapour and it precipitates or condenses out.
In the places where these systems are being proposed, the atmosphere is not pulling energy out of the water vapour and thus causing it to precipitate. Therefore, the solution is to extract the energy from the water, thus causing it to condense.
It takes a lot of energy to vaporize water. For example, to vaporize 1kg of water requires:
2500000J @ 0C
2453000J @ 20C
2256000J @ 100C
In order to condense the water, you must remove that amount of energy. One way of doing this is with a refrigeration system of some sort which moves heat from a cool plate to a hot plate.
We tend not to use Joules because energy doesn't care about time. We prefer to use a timed measure of energy - such as kWh: 1 kWh = 3600000J of energy over 1 hour.
Why would you get less water from a higher relative humidity?
How much water the atmosphere can hold depends on temperature. Consider the following quantities of water in the atmosphere at 100% humidity levels:
4.89 g/m³ @ 0C
17.3 g/m³ @ 20C
30.4 g/m³ @ 30C
At 0C, 90% relative humidity, the maximum amount of water you could extract from a cubic metre of air is 4.89 x 0.90 = 4.40 grams (about 4.4ml).
At 30C, 30% relative humidity, the maximum amount of water you could extract from a cubic metre of air is 30.04 x 0.30 = 9.12 grams (about 9.1ml).
While the paper references to papers it is pulling its number from, it seems the authors are not clear on what they are talking about and don't seem to understand how to present the data in a coherent manner. IMO, it reads like a "publish or perish" filler fluff.
Data on Heat of Vaporization:
Data on Maximum Water Content vs Air Temperature: