The economy in war torn Europe was shit. Even before the war ended, people traded stuff rather than currency. Like instant noodles are the de facto currency in some prisons today, nylon stockings were as good as money back then. Same with cigarettes. So if they didn't need it to survive in the rubble, they could trade it for food with a well meaning local.

Nylons if worn under the uniform do a great job of keeping you warm and prevent chaffing.

There's a popular magazine where I live that has a section for reader submitted "hacks" and it's kind of infamous for how many of them utilize nylons in some shape or form.

I'm quessing it's not for any single purpose but rather a light and multifunctional item.

I'm sure there were good reasons that others have noted, but I find there is usually a good reason as well as a real reason for all human choices, and when it comes to nylon and WWII, it's hard not to think of the DuPonts and their influence in the early military-industrial complex.

Who knows in what smoke-filled boardroom some wonk was instructed that "nylons will be part of procurement for survival kits, your job is to figure out why"? I speculate here, but it would be fully in character for them.

Giving her nylons could turn a hardcore nazi woman into an Allied collaborator in about 5 seconds.

They can help prevent chafing and blisters. They're a good base layer under thermal underwear. They can keep some insects, leeches, and other parasites from biting.

US Soldiers in Iraq commonly requested family members send pantyhose in care packages.

For a pretty good weekend in Vegas.

Could be part of a water filter or used as mosquito netting but it doesn't hurt to have something worth trading if you end up in a populated area too. They're lightweight, multi-purpose and valuable in the kind of place where a damaged bomber might make an unexpected landing.

It was an easy way to get your dick wet in post war Europe.

Trade good. Cheaper than gold.

Tourniquet?

Edit: found this: https://sofrep.com/news/nylon-stockings-were-once-used-to-win-the-war/

It's paywall for me, but there is an archive link.

first guess, lightweight portable water filtration

Hey now, don't kink-shame downed pilots. It's just the way they like their lovin'

Sauce: pielot

My probably very incorrect guess is to hide syphilis signs.