I have an Ikea sandbacken sofa with supposedly washable covers. I’ve washed them, ironed them while damp, and put them on still slightly damp.
The difference between the photo on the Ikea site and the “rumpled linen” look I’ve got is laughable.
I have a really good steam iron that makes light work of most things but this has defeated me.
But in general, the stuff you buy in shops has this crispness that I can never match afterwards. There must be a secret to it.