Depending jpon time of year and climate in your location, leaving damp items laying about waiting for ironing, even in plastic can cause disaster. That is mould and or mildew stains, which by the way are nearly impossible to remove totally if severe.
Yes, placing items in the fridge does by some time, but not long as one thinks. Remember foods go mouldy whilst sitting in there as will damp laundry sitting in a sealed plastic bag.
Personally find it better to take items from either the extractor (spin dryer) of the Hoover TT or "Spin-X", or out of the Miele and they are nearly always near or ready "damp dry for ironing". There are some things that one does not extract too long or even at all. These are allowed to drip dry but not until they are totally dry. Just enough moisture remains in some areas that once folded and allowed to sit for a bit will evenly distribute all over.
Oh and another thing, though common house-keeping lore suggest rolling items up tight after dampening, it is not always best. Better to fold things carefully best to allow moisture to evenly spread out. Also the smoother you keep things before ironing the less work there is to do,regardless if it is by machine or hand.
L.