Well, someone has.
GreenCore Air has come up with the solar-panel powered AC that can cool a 600 square foot room and is powered by a single 170 watt solar panel.
It already runs on DC power, so there's no need for users to put an AC inverter between the solar panel and the air conditioner, sparing any power loss while converting AC to DC.
The only AC power is to recharge the batteries at night when the sun goes down. But the more solar panels and/or batteries added to the system, the less AC power required for battery charging.
The solar panels charge the batteries and the air conditioner runs off the power stored in the batteries. Depending on outdoor temperature, thermostat setting, global position and season, the system will run for four to eight hours before automatically switching to allow the batteries to charge from standard AC grid power. When the sun is not out the unit runs on the battery bank which is integrated within the unit.
The power required to charge the batteries is far less than the power required to run a conventional air conditioner. A full charge is complete in about three hours, and it keeps working during the charging process.
Prices start at $5,700, depending upon the model. The mobile unit comes standard with a solar panel top lid of the box, but you can add more. The US Navy has picked up some for their more offgrid locations in faraway places.
GreenCore Air says you could run this off a wind turbine too, but I expect that if you have enough wind, you probably don't have the problem that this invention solves.
Photo by Flikr user yezi9713