When this feature was introduced by Whirlpool, new "miracle fabrics" were being sold.  Many people still did not have clothes dryers.  As Tomturbomatic has stated in the past, wash'n'wear cycle pioneered by Whirlpool were most effective with these new fabrics particularly for folk who still ine dried.  Maytag's 900 (all-button) models did have a W'n'W cycle with a partial drain and fill with cold water cool down.  When they finally did come out with the function on ordinary timer dials in the very late 1960s, it did partial drain and refill with cold, at least once, if not twice.  the commercial FabricMatics did one of those that took the place of the portion of the post wash spin that led up to the spray rinse.  the spin that followed was the period that followed the spray rinse also.  So Maytag didn't agitate after refilling just like initial Kenmores and Whirlpools.  Just partial drain and refill about 4 or 5 times.  My 1977/1978 GE did actually have a true partial drain and refill with cold and agitate before spinning.  but the agitation period following that cold fill was 6 to 8 minutes long (I timed it, it seemed excessive to me).  But that was short lived with GE, a friend from work got basically the same model I had the following year and had reverted on the timer dial back to the old begin extended spray rinse as soon as pressure switch was reset as water drained out of the washer and sprayed until the time for the rinse fill.   I think it was still pretty effective because it began spraying long before spin speed ramped up.  I THINK the Frigidaire 1/18s also had a cooldown, but on their PP cycle (as well as Knit), it did an extended spray rinse and with that Jet Circle Spray system, clothes got saturated with cold water pretty quickly once it started spraying.  Also, the spin speed on those cycles were hardwired to be slow. 

I still use the equivalent on my WP Duet.  It particularly comes in handy when I use steam option for heavy soiled poly-cotton dress shirts as well ass my white dress shirts (hot water then).  It does a 2 minute water mill at the end of the wash or steam part of the cycle to cool down the load.  If I don't use steam or hot, just warm, I have another cycle that's very "European", how it approaches it task, for said type of garments with warm water.  It doesn't do any spins after the wash and does 3 rinses.  My old Frigidaire did something very similar for its colors/wrinkle free cycle. 

Well Steve, if you were using a WCI58 or WI57 and a cold rinse, that's the same thing with the wash overflow rinse.  Why I would consider a WCI58 pretty much an all-fabric washer because of the water temperature options. 

Synthetic fabrics, I washed a lot of my family's clothes in the late '60s and through the '70s, much of which was, yech - 'permanent press'. As I was also responsible for pressing the clothes, I had a very high motivation to figure out the best way to launder the nasty stuff clean and as wrinkle-free as possible.

Here's what I learned. I don't see why it would have changed today:

1) Thermal shock is not good for polyesters, acrylics aren't as bad.

2) The cool-down cycle followed by a warm tumble dry (but not too dry) and with half the dryer's capacity, actually did leave things nearly wrinkle free.

3) The nonsense about dry ironing was stupid. A steam iron got things pressed faster and better than did a dry iron. I don't give a flying fig about all the hydrogen bonds not being there, etc. Whether it be the heat of the steam or the moisture or whatever, shirts came out much better and faster with steam than without.

Perhaps the most useful thing I learned, though, is still useful today - my dad's shirt collars were never cursed with 'ring around the collar'. I asked our home-ec teacher why this might be. She answered me with a question: How often does your father bathe? Twice a day, unless he's been working in the garden I responded - then more often. Ah, she replied - there's your answer. Ring around the collar is the result of dirty necks, not any particular fabric.