If we are using shore power, why don't we use a potable air conditioner and vent the hot exhaust out a vent? Why do we need a seawater cooling system for AC? Is it space? Interested in your opinion!
Air conditioners (and refrigerators) work by pulling heat energy out the air in your house/cabin, and dumping it somewhere else. For a window or portable AC like you see in homes, they dump the heat into the air. That's why the part of the AC which sticks out the window blows hot air.
A boat presents an interesting tradeoff because water has over 3000x the heat capacity of air for a given volume. That is, if the AC normally requires 400 CFM of outside air (about how much is pushed by the big fan in the outdoor unit of a residential central cooling AC), it can accomplish the same amount of cooling with less than 1 gallon per minute of seawater. On top of that, seawater tends to be cooler than the air (during the day when you're most likely to be running the AC), which improves the efficiency of the AC unit and can reduce the amount of water required even more.
So it boils down to a choice between a simple install with a big fan blowing a lot of air, or a complex install with an inlet and pump which only needs a little water. For any substantial cooling (larger boat, higher heat load like with an engine), water cooled is always preferable. But for a smaller boat the simplicity of a window or portable AC unit may be more desirable.
There is a type of portable AC which dumps the heat (or tries to) into the water it pulls out of the air as it dehumidifies. You can tell them apart because they don't have a hose to send hot exhaust air or water out the window. I don't have much experience with them, aside from knowing you need to empty the water tray occasionally or it'll overflow.
Also note that air conditioners are just heat pumps. If you get a reversible one, it can work as a heater in the winter. In that case it'll be pulling heat energy out of the seawater, and transferring it into the cabin air. The water will also tend to be warmer than the air (in winter), making it operate more efficiently in this capacity as well than a heat pump venting to the air. Heat pumps tend to become inefficient when the heat sink drops below about 40-50 F, and most of them come with an electric heating element which kicks in when the temperature gets too low.