Pillows are a hot commodity in my area, not for EMS per se, but all the ED's. We exchange linen at the hospital and if there is no pillow on the bed we're offloading to then we won't have one unless we take it from the patient. Generally I use an extra blanket folded up for the head and keep our pillow under the bench. If we get a long transport, or need it for splinting, or have a patient who is particularly uncomfortable (kyphosis, chronic pain, etc) I will pull it out. Unfortunately due to logistical realities I can't have a pillow for every patient and I do pick and choose when to use it, knowing I'll likely lose it.
As far as hygiene goes, the pillow is vinyl. Remove the case, virox the pillow and put on a new case; problem solved.