I agree that having a clothesline in the yard tends to speak "poor" or "low-class", at least in U.S. It's viewed as: You dry clothes that way because you don't have money for an electric dryer (but, truthfully, a lot of the houses next to the clothesline reflected that poverty).
I know what you mean about the softness and wrinkles, but one thing I do like to have line-hung are bed sheets. It just seems like they smell fresher than out of a machine.
Another memory: Being chased by bigger kids, and I was able to run under the clothesline, no problem, but my pursuers would either have to duck down or strangle themselves against the line. I also remember hiding behind a sheet hung from the line . . i.e., game of "hide and seek" . . but you have to have the sun on the sheet side rather than from where you are crouching, or your shadow would give your location away.
Wow, the things we remember, if given enough chance!