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Plus if you have AC then the AC has to dehumidify the air first before it can cool it.
That isn't how AC's work. They work by using the fact that a phase change between a liquid and a gas is endothermic. It turns a refrigerant into a gas and that sucks heat from the air in your house and then pumps that gas outside to cool off with your compressor, moving heat outside. (Someone correct me please if I got details wrong). The act of pulling that heat from the air into the phase change cools down air and water condenses out of the air, dehumidifying it. Fun fact AC's weren't designed for our comfort, some facrory needed less humid air for their product, us lazy workers cooling down a little is a side effect.
https://en.wikipedia.org/wiki/Enthalpy_of_vaporization#:~:text=used%20among%20others.-,Enthalpy%20of%20condensation,-%5Bedit%5D
The cooler air converts the water from a gas to a liquid which generates heat. The more water in the air the more heat gets generated. You don't really get as cool of air until the air has been dehumidified.