combining a humidifier with refrigeration cooling, what do you think?

As the air gets dries it gets less efficient for the AC to reduce the temperature.

Each watt of energy gets rid of fewer BTU as the air gets drier.

This sounds erroneous to me.

As this vapor moves to the AC, you need very little energy ( dew point ) to turn it back to water.

That doesn't sound right either.

Without this extra mist humidity, the AC would pump the heat through its internal refrigerant.

Likewise.

I think this theory is built on a faulty assumption. Also, if it were this easy to do, they'd be doing it.

It sounds like lots of half baked theory with no experience. If you run water over the coils of a standard unit it will do 1 of 2 things depending on the water. Condensate will end up etching the aluminum fins and causing leaks in the system. Using house hold water source will build up on the fins reducing the heat exchangers ability to reject heat in the system both are bad and limit the life of the coils.

Large chillers use falling water to keep the condensers cool but this is buffered and treated water to prevent legionnaires (the original source of the disease) These are large systems and designed to take advantage of evaporation the cooling tubing. the ones I have worked on have no aluminum some are copper and some are steel. The water has a glycol and other buffers to prevent freezing and the ph is stabilized and controlled to prevent organically from growing.

Heat pumps don't easily drop humidity below 40% rh. In my experience living in a humid area, it's more like 55%. Swamp coolers put out air around 95% rh, much higher than typical outdoor humidity even in humid areas. So while the air may indeed be even cooler, your sweat won't evaporate as well (same as if you were outdoors), and so you would feel hotter than only in the AC - if you've ever been in dry heat, you know what I mean. Even in a room successfully cooled to 65°F, 95%rh would be uncomfortable to work in because you just wouldn't stop sweating.

Not to mention the interior surfaces of your AC will probably have condensation develop on them, as well as other nearby metals, leading to corrosion and other moisture problems, and an increased general risk of mold and mildew.

The best way to boost the efficiency of an AC in my experience is to circulate the air in the cooled space using a high velocity fan - move the cooled air away from the AC and the hotter air towards it.

One does not simply ignore thermodynamics ;)

As this vapor moves to the AC, you need very little energy ( dew point ) to turn it back to water.

Latent heat of evaporation works both ways. You need to provide 683 Wh (Watt*hours) of energy to turn 1 kg of water into water vapour... and if you have one kg of water vapour, you need to suck the same amount of energy out of it to turn it back into liquid water. You can view condensation as "pumping heat out of water vapor", or "whater vapor heats whatever it condenses on" but the way to visualize it does not change the physical phenomenon, which involves an amount of energy (heat) corresponding to the latent heat of evaporation.

If you use a mister to evaporate water, it will take the energy from the room, but it will return this energy to the AC unit as the AC unit condenses it back to liquid. From the point of view of the AC unit the only difference would be, maybe, a little bit better heat transfer on the evaporator fins.

So it shouldn't do anything to the electricity bill, but it will make the room moister and less comfortable.