I have a book at home (I'll track it down and post the title on edit - Edit: The book is "Simple Socks" by Priscilla A Gibson-Roberts) which gives sizing rules and patterns for knitting custom fitted socks. I am hoping to be able to convert the hand knitting instructions to sock loom (hand knits are usually turned, as best I remember, so that knits and purls would need to be interchanged on odd - or even - rows for the knitting loom, since you always work the "right" side of the article on a knitting loom; whether there is any more to this pattern conversion, I can't remember - increases and decreases might need some finessing, too). My mother made sure all of us kids knew how to knit, crochet, sew on a button, weave on a frame loom (potholders, mainly), darn socks, make gravy, etc. It's been a while since I have knitted anything, but I just sewed on a button the other night (I used a
wood screw, not a match stick, to space the button out from the shirt - that probably wouldn't have passed muster!). I have a large Knitting Board loom, and a small KB sock loom, both obtained used, but in as-new condition. Knitting is a winter
project, so it's all back burnered while I try to beat the turn of the weather on outdoor projects.
(As an aside, I have a friend - now in his early 80s - who ended up being a medic in Vietnam because his drill instructor noticed that he sewed a patch on his uniform with some degree of skill compared to the other draftees. Since he could sew on a patch, he was a shoo-in to sew up the wounded, and that was that. I'm sure his mother had no idea how handy her sewing lessons would prove to be! He parlayed his compulsory service into an engineering degree via the GI Bill, went on to grad school and a PhD, then taught a couple of generations of engineering students vehicle dynamics and - eventually - hybrid vehicle design.)
In any case, the aforementioned book gives a pattern for making socks with replaceable heels and toes. That is, you can unravel and then re-knit heels, toes or both, while the basic structure of the foot and cuff remains stable. This allows you to replace (rather than just darn) the entire heel or toe of a sock, which tend to be the high wear areas. I usually wear out heels, but other people, with different bone structure and footwear, may wear out toes first. This is not to denigrate a proper darning job (look up Swiss darning on YouTube for instructions, if unacquainted), but there is only so much you can do, at some point. Knitting socks which are suited to an in-frame overhaul from the outset is an interesting idea.
I am a big fan of wool or wool-blend socks, but I tend to have sweaty feet and live in a cool temperate climate (winter temps rarely colder than 0F/-20C, but sometimes -25F/-32C during a cold snap). If someone did not have this personal quirk or lived in a warmer climate, cotton,
linen or hemp might work just fine. The old "Wigwam" ragg wool socks (I think they had ~10% nylon, the remainder wool) used to be very long wearing for me, but the last couple of pairs have exhibited a disappointingly short life. I'm not sure if the socks have changed, or if I (or my footwear choices) made the difference. In any case, I have pretty much given up on them.
Another possibility, but much slower than knitting, is nailbinding (nalbinding, with a little circle diacritical mark over the "a"). Unlike knitting, this uses what is basically a single darning needle to loop the yarn through the existing work - sort of a loopy blanket stitch. Short sections (~6 feet or 2 meters long) of yarn are traditionally joined with a "spit splice" - ends of yarn sections felted together - to continue the work. If using something other than wool (which cannot be felted together), the joins can be knotted together, but for socks, I don't think you'd want the knots underfoot, so wool would be the preferred choice, I think. The advantage of nailbinding is that it will not unravel if the yarn breaks when snagged. Very hard wearing, and has been used for something like 4000 years to make socks, mittens, hats and other outerwear. There are some threads on these forums about nailbinding. I haven't played with it in any serious way, I just know of it. As in many things, I'm a bit of a dilettante in this area of endeavor, as well.
An old-fashioned approach to dealing with worn socks was to wear long knitted tube socks. After you wore through the heel, you'd rotate the sock around your foot 180 degrees. After you wore through that, you'd chop off the worn out parts, and re-tie the toe to lather-rinse-repeat the cycle. I've never done this, but I've seen mention of it in
books about sourdoughs - miners and trappers and so on in the Far North. I prefer socks with some shape to them, not tube socks, since I - tenderfoot that I am - can't stand to have wrinkles or creases in my socks, whether on top or under foot. People were clearly made of sterner stuff in the old days - born with the bark on 'em!
I have seen videos on YouTube of people disassembling high-priced designer wool sweaters acquired from thrift stores to salvage the yarn to remake into other projects. Sometimes, fine gauge yarn is "plied" to make thicker yarn, more suitable for the new purpose. Depending on how the sweater (or other larger article of clothing) was manufactured, you might end up with some short lengths of yarn near seams. Many higher
class articles are made as completed knitted panels with all of the shaping built in, then joined together. Cheaper goods may be knitted as generic flat
yard goods, then cut out and sewn (or maybe sewn, then cut?). This is beyond my ken. Anyway, it seems very thrifty and resource mindful to repurpose yarn from one article of clothing to make another.
Regarding cotton: I am reliably informed that there have been huge strides made in the culture of cotton by using Johnson-Su
compost extract on broad-acre cotton fields in Turkey. This may help to make industrial scale cotton agriculture more sustainable in the future.