Here is another question for folk who wash new clothes and other fabrics: what do you do if you buy something which is dry clean only? Surely if you take it to a dry cleaner for cleaning it will become 'soiled' by others touching it? I'm being devil's advocate...
Also - and maybe we have covered this, it must be very difficult sleeping in hotel beds knowing other people have touched the sheets.
You seem fixated on the "somebody else touched it" aspect of this. There are other reasons as well, like just to freshen something up, or to get the deeply-set wrinkles out that a shirt that's been folded and packed in a wrapper for months has. Sure, it could be ironed, but to get those wrinkles out takes a lot of ironing, or a 15-minute spin on my quick-wash cycle. I know which one I'm choosing!
I'm assuming that during the manufacturing process clothes/linens/towels are washed a few times, to set the dyes, to pre-shrink, etc. once an item goes to shipping and then makes it to the shop floor, it's probably spent considerable time in dusty warehouses, and dirty shipping containers, so washing it once is just a way to knock all that bit of dust and dirt off, and get it smelling more like something clean, and less like a warehouse, cardboard box, greasy truck, or whatever it is a department store smells like.
I have some clothing items that are seasonal. From about November to March, I take out several cold-weather items from a couple of plastic bags that have been packed away, I put in several warm-weather items. What's the first thing I do with the items I unpack? Into the wash, just to liven them up a bit.
As for dry clean only items - before I wear them for the first time, they go to the dry cleaners. That way, they're as reasonably clean as can be before I pop them on.