The entire world didn't have AC just a few decades ago and most people slept fine.
If in less than a century of introducing a tech your body becomes so dependant to it it impairs a critical body function if you don't have it, yes, it's a handicap.
Actually people often didn't sleep fine at all. Or let's see some evidence that they did because I don't believe you. I know my own grandparents complained about being unable to sleep soundly during the summer when they lived in New York without AC.
Complaining about not sleeping well in the middle of a hot summer is very different from not being able to sleep at all in the middle of spring without an AC.
It's pretty rare for our nighttime lows to be above 72, even in the Summer, and I live in a fairly hot part of the US (though not the South proper). Even when it's in the high 90s or low 100s during the day, which is typically only a few weeks a year, usually it still gets down to 75-78 at night. We're in the high-80s this week and nighttime lows will be as low as 58F.
Spring nighttime temps are more like 35-55.
The main trouble's the damn humidity. A very-humid 72 still feels gross. And maybe I could sleep like a baby on a night when it gets down to 60, but if that's a spring or summer night I'll wake up nasty and covered in sweat unless I've got some serious dehumidification going (that's what happens when I go camping—might be cold enough to sleep well, but unless it's Winter or late Fall the high humidity still has unpleasant effects). Plus you get mildew and mold problems if you let a modern, very-sealed-up (so, efficient for AC) house get very humid too often, so it's better to just dehumidify with the AC even if the outdoor temp matches what I'd like it to be indoors.
Well, another way I can sleep OK in most any condition (short of becoming badly sleep-deprived) is to get a ton of physical activity during the day. Wear myself right the hell out, so I'm dead-tired by sundown. I bet physical activity levels were way, way higher pre-AC, too.
If in less than a century of introducing a tech your body becomes so dependant to it it impairs a critical body function if you don't have it, yes, it's a handicap.