Cotton retains moisture, thus cotton socks will not do the job properly.
When would actually one want to wear exactly cotton socks?
A few ideas come to mind, but they are just shooting in the dark:
When would actually one want to wear exactly cotton socks?
Hygienic reasons where washing your socks hot (95 °C) and frequently is important.
I guess the most common such reason (besides being doctor/nurse/...) is having a fungal infection. In that case in addition to the proper medication you should change your socks frequently (if they get moist even more often than daily) and wash them really hot so your feet do not get re-infected next time you wear those socks and get them moist.
However, in that foot condition long hikes closed boots are not a good idea, so not sure whether this is an "outdoor" answer.
I've successfully washed synthetics socks at 60 °C many times that were rated at 30 °C, but never tried out how they take washing at 95 °C.
I wear cotton socks a lot in everyday life, in winter also woolen socks. I prefer synthetic or wollen socks for longer (several days without time to properly dry boots) hiking tours because I'm afraid once the whole foot-sock-boot business is thoroughly moist (the only time I didn't get moist feet on hiking/skiing so far was a winter spent in Manitoba), the cotton socks would lead to more blisters because they are usually less soft/smooth than the woolen or synthetic socks.
As to the retain moisture part, I'm not so sure how much that matters in a closed shoe/boot scenario: usually it is much easier to dry a cotton sock than getting the corresponding moisture out of the shoe.
(I guess that is what you were driving at with the not fill the shoe with salt and grease sentence? - though for a leather shoe grease would probably be good, but neither salt nor moisture is.)
In the office, I keep a spare pair of (cotton) socks in case I get really soaked biking there (I prefer to change also synthetics socks if they are thoroughly wet). I rarely have cold feet, and drying cotton socks on my feet that are slightly moist after the bike ride to the office is no problem once I've changed the shoes (when sitting at the computer, I usually slip out of the office/lab shoes).
Yes they do have a decided price advantage, and in my experience they last at least as long as the synthetics socks. My woolen socks last longer but then I wear them less frequently.
If outdoors includes activities where you return indoors in the evening: I often wear cotton socks when working outdoors. I don't see a big difference whether I have to wash the socks because they are dirty or because they are dirty and moist.
I carry a pair of cotton socks on every backpacking trip for one reason: To sleep in.
After a day on the trail, nothing like a dry pair of comfortable cotton socks to absorb all that foot moisture and leave your feet toasty dry by morning. Helps keep your feet happy and healthy.
Bonus ProTip: A cotton handkerchief wedged in other "moist" and chaffing areas can have similar drying and healing advantages.
Availability factor - cotton socks you can buy practically everywhere.
When it comes to price, the wool socks you can buy relatively cheap in the military surplus, but it usually means buying in internet. Wool socks are good for winter, but for me they are not-an-option in summer because my feet sweat in them like mad. Wool socks are also heavier and taking much more place than thin cotton socks.
For summer, an alternative to thin cotton socks are the syntetic ones (I haven't seen thin wool socks). Then the price comes into play. Maybe there are simple, cheap syntetic ones, but I know only those 'active' ones from sport shops - they are very expensive compared to cotton ones - about 5 times more. So in summer, I prefer to take more cheap, light cotton socks and change them more often.
I would just like to add a comment about your "in the summer" bullet point.
A few years ago I went to the southwest to hike in Utah canyon country. I had some smartwool socks. I wore a clean pair every day in the 100+ heat. They kept my feet nice and cool and dry.
One morning I wondered if they were really making a difference; so, I wore cotton socks and took a pair of the smartwool along. My feet quickly became sweaty in the relatively cool of the morning as I started the hike. I changed to my smartwool socks.
Now, the smartwool socks are a lot more expensive than cotton socks. So, it is probably not practical to wear them every day. But, for long hikes in hot or cold weather, the smartwool performed wonderfully for me. And, I need to add that I didn't have the thin smartwool socks. I had the regular thick ones. I wear them at home for long hikes in the parks.
I will also add that I wear cotton socks daily. They are relatively inexpensive. It is easy to have a spare pair around to change into if your feet get wet or sweaty during the day.
