Technically (🤓), you don't have to wash your hair because it's dead. The scalp is where the sweat, oils, and skin cells build up and where the bad odours would be coming from. And most people on average aren't really close enough to someone (especially a tall someone) to smell their scalp.

Personally, I tried the whole no shampoo thing, and it was agony. The roots of my hair hurt from the build-up if I don't wash them once week, only rinsing with water does nothing. Human bodies are weird.