I didn't see anything related to removing allergens from the hair.
If you have (or suspect you have) allergies to dust mites, dogs or cats, pollen, fungi (mold) -- things that blow around in the air and sit on surfaces, you will feel better if you at least rinse your scalp after exposure to those things! And at least during your allergy season -- unless you've got year-round allergies like I do. Allergies can cause itchy scalp systemically, but the contact with allergens in your hair and on your scalp can give cause itching etc. as well.
It also helps to have an allergen-proof pillowcase and mattress cover and wash sheets weekly, either in very hot water (130 degrees, hotter than most of us have our water heaters set) or to add 30-50 drops of tea tree oil to the wash cycle to kill dust mites. (the scent goes away when the sheets are dry)
Dust from roads and fields and calcium chloride used to control dust are also irritants that need to be rinsed off.
Because some of these allergens will "stick" to your scalp/hair, sometimes a shampooing (co-wash... I'm not sure) is the only way to get them to go down the drain.