Cotton/Polyester, Polyester, even Nylon Bed/Table Linen
Are not new, they exploded onto the scene during the 1960's "wash and wear" craze on both sides of the Atlantic and elsewhere.
Housewives fed up with ironing bed and table linen and or sending it to laundry were supposed to be delighted with these "no iron" or "easy care" products. In reality the truth was often different than theory.
Yes, many did like them others found sleeping on such things horrible.
Neither polyester or nylon breathe so just as with those horrible leisure suits things turned into a hot, sticky, clammy mess. Then there was the problem of laundering. As noted above polyester does not like water and tends to hold soils/oils. So after awhile linens turned yellow and or tattle-gray. Excessive use of hot or boiling water was O-W-T unless an excellent cool down process followed.
Being as all this may some persons then and now swear by cotton/man made fiber blends or pure man made fiber (such as nylon) bed linen. Have friends in Europe whose mothers and grandmothers think such things are the cat's meow.
Regarding table linen again to cut down laundry costs much of what is sold/rented for commercial or purchased for domestic use is poly/cotton blends. This applies at least to middle and lower price points and in some cases reaching into the high end. People either don't want to iron their linens nor pay someone else to do it either.
This being said a small percentage of polyester does make for bed and table linen that is easier to iron even by machine. Many hospitals have long chucked pure cotton muslin sheets in favour of a cotton/poly blend. This demand can and has often come from their laundry and or whomever they rent their linen.
Cost savings come in part because the addition of polyester makes for lighter linens, and since commercial laundries largely charge by the pound even a small percentage reduction in weight can make a huge difference. This is especially true when one has laundry bills for hundreds of pounds of wash per month.
The addition of polyester also means less heat/energy is used for drying and or ironing since both must be done at lower temps. Also with the addition of polyester there is less creasing as compared to pure cotton hence a reduction of the need to iron at all. Feel sure some places simply "wash, fluff, and fold".