I would give up Internet before I gave up A/C. I've only seen one home in Tucson well enough insulated to give up A/C, and it was built, brick by brick by the owners, and only had two very small windows.
As with everything, there are pros and cons--cheap electricity has simply led to the use of AC rather than natural cooling.
People live in the tropics without it. It is not a necessity.
I can hardly do anything but think of ways to get away from the heat (cold shower, going into the shade outside, going someplace with A/C) and falling asleep usually takes about four more hours than it should as I wallow around like a pig. Every 6-month 100-degree summer reminds me why I need to move out of the South.
He had a ceiling fan but no AC. So he would wrap himself in a blanket until he was soaked with sweat. Then he took the blanket off and laid on his sheet and let the fan blow on him thereby evaporating the sweat. This would cool him down and allow him to sleep.
In the past, people were allowed to sweat (and smell of sweat.)
Even still, there are countries far hotter than the United States which do not generally (or never) have A/C and they seem to survive just fine. Perhaps the definition of "necessity" is the argument here, but in a strict-leaning sense, A/C is hardly a necessity. None of the things on that list are, really.