I think I was the first one that mentioned it being illegal. I don't live in an HOA. It is actually the city that has banned it. I think that this city is a tad bit ... pretentious. I think it is just one of those local things. They also have a rule that all new houses have to be at least X% brick exterior. I would guess around 70%. Some places, none of the houses are brick and they look fine. But, in this city, people would think about a new wood house, "Why didn't you save up a little more money and buy a real house?"
Of course, when our drier died while we were cloth diapering our baby, the law didn't stop us from stringing twine ALL over the backyard. I actually think the neighbors would not worry if you put a clothes line in your fenced back yard. Houses are single-story in my neighborhood. If you did not have a fence (rare), and a clothes line they would probably complain. But more because the clothes line would give them an excuse to complain since you aren't required to have a fence. Although, I have figured out that the garbage guys get bonuses for reporting people with too long grass. We have an alley so the garbage truck goes down it. They might report a clothes line in a fenced backyard hoping to get a bonus. Nobody said anything about the twine all over our backyard. Although, seeing about a 100 old-fashioned white cloth diapers hanging from twine strung from the frame of the bench swing to a tree branch to the fence to another tree branch, etc. anyone would know that our drier died and that was a temporary fix.
The drier is such a tiny part of my electric bill, cost is not a consideration. I hang my clothes on a hanger because it is better for them, and I'll be hanging them eventually anyway, so no extra work. We are remodeling an old house and when I saw that the laundry room and the master closet shared a wall, I insisted on a hole between them and a clothes rod through the hole. I can hang up my clothes in the laundry room, and then dry, just shove them into the closet.