I'm also never willing to air dry sheets or towels. They're too big and hold too much water to dry properly in any climate I've ever lived in.
One thing that occurs reading this: Climate issues aside, how fast do US washing machines spin? I know they're different, what with the top loading thing and all, so I wonder if they don't spin as fast as our front-loaders and don't get enough moisture out to make line drying effective.
I use a front-loading washer where I live now that is probably comparable in its features to washers commonly available in other parts of the world. Before it got old enough that we were concerned about it breaking on us, we would typically spin the clothes at the top speed after washing (1200 rpm). That got normal clothes to that just-damp stage, and it's rare for things like shirts or pants to take more than a day to dry once we hang them up.
But that's normal clothing. Towels absorb a lot more water, and sheets are very large, so neither of them would be likely to dry properly within a day. If they stay damp much longer than that, they'd start to smell weird. I live in a part of the US that is very similar to the UK, which means drying things outside in the winter is pretty much a no-go (and my apartment is not heated with radiant heat, so there's no help there). I'm not about to air dry clothing outside in the summer, because we have a lot of pollen in this area and it gets on everything
. I'm not allergic, but it makes things dirty.
Where I used to live, the climate was basically tropical for 9 months of the year, and torrential rain storms were common year round. I still hang up some of my clothes to dry when I do laundry at my parents' house, but even with air conditioning serving to de-humidify things inside, my stuff takes twice as long to dry.
As far as electricity in the US, it is absolutely cheaper. Given that I don't pay an arm and a leg to use a tumble dryer, and that my time and effort are not free, I frequently choose to tumble dry laundry.