There are three reasons for neck feather loss Anni D, one of which is a partial neck moult induced by stress which could be due to inadequate space. I agree that should be ruled out if they all seem happy. The second is pecking due to boredom, but that would be only affecting one or two at the bottom of the pecking order. The third is something called 'depluming mites' which dig into the feather quills to suck the blood out. This causes a lot of irritation to the extent that the affected hens welcome the feathers being pulled out. They would be spread by contact and it is the front of the neck that rubs against feeders and drinkers, so perhaps that is the cause?
The treatment we would apply, as we have in the past, is a light spray (0.5mL) of Frontline in the area. If it is anywhere near the eyes we don't risk a spray and use a cotton bud to apply it. In England you can only get Frontline spray from a vet, whereas here we can buy it from pet shops. It isn't licensed for chickens but we've used it with great success for years without any adverse affects. It is particularly good for Northern Fowl Mite, which I hope you never encounter.