We always had a massive laundry pile cos my mother was obsessed with ironing everything. It was ridiculous. She never seemed to be able to grasp that if you fold stuff when you take it off the line, 95% of it doesn't need ironing. And we never cared anyway. It was her thing. Then she would make me and my sister iron most of it. As a result, I hate ironing and haven't ironed anything in years.
I gave up ironing shortly after we came to Australia. Like you say, only a fraction of things even need it, as long as you dry them hanging flat and put them away, they're fine. I feel like it's an English obsession. These days everyone seems to have super fancy steam iron stations over there.
My mother was English so that makes sense.