Gosh, I'm the ONE voter that irons just about all our fabrics!!
The scent of ironing and the hot fabrics takes me back to sitting with Mom as she ironed our clothes (ah, Faultless Starch!) each day, after school. Dad was Air Force and uniforms had to be ironed. She ironed our table linens and all my dresses. This was in the days before perm press clothing and we never used paper napkins.
I love to iron and find it wonderfully relaxing. I iron after things come out of the dryer (while they're still the tiniest bit damp), so every few days. Things look so nice, crisp and bright.
Excepting winter coats and ski gear, all our clothes are ironed, even t-shirts (no, I don't do underwear or bras!). Yup, jeans, too. I iron our table linens (tablecloths and placemats, as well as napkins - we avoid paper napkins, if possible).
I iron our sheets, as well. I use lavender essential oil in my water misting bottle and everything has the wonderful fragrance in it. Whenever we have guests, they always say how much they love the feel of the perfectly smooth sheets and the fragrance!
I don't buy any perm press clothing or other item that are listed as "wrinkle-free," if I can avoid it (we don't want the chemicals in them).
I also sew, so ironing is important for that, as well.
I'm amazed at how many do not even own an iron!