In my area, where relative humidity is often 60-90%, this form of drying would result in moldy cloth, not dry diapers. My guess is Tampa's microclimate is probably similar and line drying isn't an option.
Mold thrives in moist, dark places, not most sunny ones.
Also the society functioned differently; one middle-class salary could sustain a middle-class family, for one.
We no longer live in that reality, nor would anyone want to.
It's like saying that homeless people are OK because there were no buildings in prehistoric times.
Edit - and having lived in both, you're much better off drying things in a hot humid place than in colder ones.